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| == New Balance Femme etc. Show this message to Dr. == | | {{Infobox scientist |
| | |name = Hans Georg Feichtinger |
| | |image = Hgfei class2011.jpg |
| | |image_size = |
| | |caption = Hans Georg Feichtinger teaching |
| | |birth_date = {{Bda|1951|6|16|df=y}} |
| | |birth_place = [[Wiener Neustadt]], [[Austria]] |
| | |death_date = |
| | |death_place = |
| | |residence = |
| | |citizenship = |
| | |nationality = |
| | |ethnicity = |
| | |fields = [[Mathematician]] |
| | |workplaces = [[University of Vienna]] |
| | |alma_mater = [[University of Vienna]] |
| | |doctoral_advisor = [[Hans J. Reiter|Hans Reiter]] |
| | |academic_advisors = |
| | |doctoral_students = [[Peter Balazs (mathematician)|Peter Balazs]] |
| | |notable_students = |
| | |known_for = [[Gabor analysis]]<br>[[Modulation space]]s<br>[[modulation space#Feichtinger's algebra|Feichtinger's algebra]]<br>[[Feichtinger conjecture]]<br>[[Coorbit theory]]<br>[[Wiener amalgam space]]s |
| | |author_abbrev_bot = |
| | |author_abbrev_zoo = |
| | |influences = |
| | |influenced = |
| | |awards = |
| | |religion = |
| | |signature = <!--(filename only)--> |
| | |footnotes = |
| | }} |
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| | '''Hans Georg Feichtinger''' (born 16 June 1951) is an Austrian mathematician. He is <!-- associate --> Professor in the mathematical faculty of the University of |
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| | Vienna. He is editor-in-chief of the Journal of Fourier Analysis and Applications (JFAA) and associate editor to several other journals. He is one of the founders and head of the Numerical Harmonic Analysis Group ([[NuHAG]]) at University of Vienna. Today Feichtinger's main field of research is harmonic analysis with a focus on time-frequency analysis. |
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| == New Balance 990 Burgundy ANNA NICOLE SMITH. Furthermore == | | ==Biography== |
| | Hans Georg Feichtinger was born in [[Wiener Neustadt]] where he graduated from the [[Gymnasium (school)|Gymnasium]] and received the [[Matura]] "summa cum laude" in 1969. In the same year he started his studies in mathematics and physics. He finished his Ph.D. at the University of Vienna in 1974 under the supervision of [[Hans J. Reiter|Hans Reiter]] in 1974 with a doctoral thesis on ''Subalgebras of '''L<sup>1</sup>(G)'''''. Feichtinger attained professorship with the defense of his habilitation thesis on ''Banach convolution algebras of functions''<ref>[http://aleph.univie.ac.at/F?RN=97821762], Universitätsbibliothek Wien</ref> in 1979. Feichtinger is author or co-author to roughly 200 scientific publications. |
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| | The University of Vienna being the center of his scientific life, Feichtinger still had several visiting positions across Europe and in the USA between 1980 and today, e.g. at the University of Maryland, College Park and the University of Connecticut, Storrs. He is married and the father of four children.<ref>[http://www.univie.ac.at/nuhag-php/home/fei.php], Hans Georg Feichtinger's Homepage</ref> |
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| == Canada Goose Femme il est difficile == | | ===The NuHAG (Numerical Harmonic Analysis Group)=== |
| | In the late 1980s Hans Georg Feichtinger and Karlheinz Gröchenig conducted joint research on atomic decompositions. From 1990 on, Feichtinger investigated irregular sampling and computational harmonic analysis with Thomas Strohmer. These cooperations were the basis for founding the Numerical Harmonic Analysis Group (NuHAG) at the University of Vienna with Feichtinger as group leader. While the research project ''Experimental Signal Analysis'' is noted as the starting point of NuHAG <ref>[http://www.univie.ac.at/nuhag-php/home/research.php?show=3], The 'Experimental Signal Analysis' project at NuHAG</ref> several earlier publications and projects are listed to be NuHAG related, the earliest dates back to 1986.<ref>[http://www.univie.ac.at/nuhag-php/home/research.php], NuHAG research page</ref> Over the years, NuHAG has become a group of international importance in the fields from abstract harmonic analysis to applied time-frequency analysis and currently hosts around 40 researchers (including PhD students).<ref>[http://www.univie.ac.at/nuhag-php/members/], NuHAG member page</ref> |
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| | ===Dedication to the University of Vienna and the scientific community=== |
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| == Nike Suisse déni de service == | | Hans Georg Feichtinger is the editor-in-chief of the Journal of Fourier Analysis and Applications taking over from John J. Benedetto in the year 2000, and associate editor to the Journal of Approximation Theory (JAT), the Journal of Function spaces and Applications (JFSA) and Sampling Theory in Signal and Image Processing (STSIP). Furthermore, Feichtinger is the contact person for the [[EU|European Union's]] student exchange programs [[Erasmus Programme|ERASMUS]] and LEONARDO at the faculty of mathematics of the University of Vienna and is actively involved in workshops and conferences.<ref>[http://www.univie.ac.at/nuhag-php/program/select.php], NuHAG event database</ref> Throughout his career Hans G. Feichtinger has supervised 23 completed PhD theses, also today he is advising several students (as of June 2011).<ref>[http://genealogy.math.ndsu.nodak.edu/id.php?id=44893], Completed PhD studies under Hans Georg Feichtinger at Math. Genealogy</ref> |
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| | The scientific work of Hans Georg Feichtinger includes, but is not limited to results on function spaces, irregular sampling, |
| | time-frequency analysis, Gabor analysis and frame theory. Some of his most notable contributions are listed below. |
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| | In the early 1980s, Feichtinger introduced [[modulation space]]s, a family of function spacesdefined by the behavior of the [[short-time Fourier transform]] with respect to a test function from the [[Schwartz space]]. They have become the standard spaces in time-frequency analysis. Also, while the concept of function spaces treating local and global behavior separately was already known earlier, ''[[Wiener amalgam space]]s'' were introduced by Feichtinger in 1980, also his publications have contributed to the acknowledgment of amalgam spaces as a useful tool in various mathematical fields. |
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| | Around 1990 the joint research with Karlheinz Gröchenig lead to a series of papers, which is today referred to as [[coorbit theory]]. The theory provides a unified framework for different important transforms, e.g. the [[wavelet transform]] and the short-time Fourier transform. |
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| | Feichtinger also proposed the use of [[(Banach) Gelfand triple|Banach Gelfand triples]], especially the Banach Gelfand triple <math> S_0 \subset L^2 \subset S_0' </math> that has proven very useful, e.g. in time-frequency analysis. |
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| <li>[http://1.ts.cn/home.php?mod=space&uid=14176&do=blog&quickforward=1&id=6592655 http://1.ts.cn/home.php?mod=space&uid=14176&do=blog&quickforward=1&id=6592655]</li>
| | ===Feichtinger's conjecture=== |
|
| | Feichtinger once raised the question, whether |
| <li>[http://icomedynetwork.com/activity/p/194209/ http://icomedynetwork.com/activity/p/194209/]</li>
| | |
|
| | :''Every bounded [[Frame of a vector space|frame]] can be written as a finite union of [[Riesz sequence|Riesz basic sequences]].'' |
| <li>[http://www.harrietoneilllaw.com/node/2066338 http://www.harrietoneilllaw.com/node/2066338]</li>
| | |
|
| | This question is not only an important open problem in frame theory but is equivalent to some famous open problems in analysis. The statement above is now widely referred to as ''Feichtinger's conjecture'', a term first used by Pete G. Casazza. |
| <li>[http://www.achicourtautrement.fr/spip.php?article451/ http://www.achicourtautrement.fr/spip.php?article451/]</li> | | |
|
| | Proofs are known for certain special cases since 2005.<ref>Frames and the Feichtinger Conjecture by Peter G. Casazza, Ole Christensen, Alexander M. Lindner and Roman Vershynin</ref><ref>The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates by Marcin Bownik and Darrin Speegle</ref> In 2013 the conjecture has been proved by Adam Marcus, Daniel A Spielman and Nikhil Srivastava.<ref>Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem by Adam Marcus, Daniel A Spielman and Nikhil Srivastava</ref> |
| <li>[http://enseignement-lsf.com/spip.php?article64#forum25225209 http://enseignement-lsf.com/spip.php?article64#forum25225209]</li>
| | |
|
| | <!--===Coorbit theory=== |
| </ul>
| | The coorbit theory was developed by Feichtinger and Gröchenig around 1990. The starting point is a [[Representation theory|square integrable reprentation]] <math>\pi</math> of a [[locally compact group]] <math>\mathcal G</math> on a Hilbert space <math>\mathcal H</math>, with which one can define a transform of a function <math>f \in \mathcal H</math> with respect to <math>g\in \mathcal H</math> by <math>V_g f (x) = \langle f, \pi(x)g \rangle</math>. It is important to note that many important transforms are special cases of the transform, e.g. the short-time Fourier transform and the wavelet transform for the Heisenberg group and the affine group respectively. Representation theory yields the reproducing formula <math>V_g f = V_g f * V_g g</math>. By discretization of this continuous convolution integral it can be shown that by sufficiently dense sampling in phase space the corresponding functions will span a frame for the Hilbert space. |
| | |
| | An important aspect of the theory is the derivation of atomic decompositions for Banach spaces. One of the key steps is to define the voice transform for distributions in a natural way. For a given Banach space <math>Y</math>, the corresponding coorbit space is defined as the set of all distributions such that <math>V_g f \in Y</math>. The reproducing formula is true also in this case and therefore it is possible to obtain atomic decompositions for coorbit spaces.--> |
| | |
| | ==Selected publications== |
| | |
| | Hans Georg Feichtinger has published approximately 200 scientific articles,<ref>[http://www.univie.ac.at/nuhag-php/bibtex/], NuHAG BIBTEX database</ref> a selection of which is presented below (in chronological order): |
| | |
| | * H. G. Feichtinger. "On a new Segal algebra" Monatsh. Math. 92:269–289, 1981. |
| | * H. G. Feichtinger. "Banach convolution algebras of Wiener type" in Proc. Conf. on Functions, Series, Operators, Budapest 1980, North-Holland, Amsterdam, 1983. |
| | <!--* H. G. Feichtinger. "Modulation spaces on locally compact Abelian groups" Proc. Internat. Conf. on Wavelets and Applications:52, 1983.--> |
| | * H. G. Feichtinger and K. Gröchenig. "A unified approach to atomic decompositions via integrable group representations" Lect. Notes in Math. 1302:52—73, 1988. |
| | <!--* H. G. Feichtinger and K. Gröchenig. "Banach spaces related to integrable group representations and their atomic decompositions, I" J. Funct. Anal. 86(2):307–340, 1989.--> |
| | <!--* H. G. Feichtinger and K. Gröchenig. "Banach spaces related to integrable group representations and their atomic decompositions, II" Monatsh. Math. 108(2-3):129–148, 1989.--> |
| | <!--* H. G. Feichtinger. "Generalized amalgams, with applications to Fourier transform" Can. J. Math. 42(3):395–409, 1990.--> |
| | * H. G. Feichtinger and K. Gröchenig. "Gabor wavelets and the Heisenberg group: Gabor expansions and short time Fourier transform from the group theoretical point of view" in Wavelets :a tutorial in theory and applications, Academic Press, Boston, 1992. |
| | * H. G. Feichtinger and K. Gröchenig. "Theory and practice of irregular sampling" in "Wavelets: Mathematics and Applications ", CRC Press, Studies in Advanced Mathematics:305—363, 1994. |
| | <!--* H. G. Feichtinger, K. Gröchenig and T. Strohmer. "Efficient numerical methods in non-uniform sampling theory" Numer. Math. 69(4):423–440, 1995.--> |
| | * H. G. Feichtinger and K. Gröchenig. "Gabor frames and time-frequency analysis of distributions" J. Funct. Anal. 146(2):464–495, 1997. |
| | * H. Bölcskei, F. Hlawatsch and H. G. Feichtinger. "Frame-theoretic analysis of oversampled filter banks" IEEE Trans. Signal Processing 46(12):3256–3268, 1998. |
| | * H. G. Feichtinger and T. Strohmer (editors). "Gabor Analysis and Algorithms. Theory and Applications.", Birkhäuser, Boston, 1998. |
| | * H. G. Feichtinger and T. Strohmer (editors). "Advances in Gabor Analysis", Birkhäuser, Basel, 2003. |
| | <!--* H. G. Feichtinger and K. Nowak. "A first survey of Gabor multipliers" in Advances in Gabor Analysis, Birkhäuser, 2003.--> |
| | * H. G. Feichtinger and N. Kaiblinger. Varying the time-frequency lattice of Gabor frames. Trans. Amer. Math. Soc., 356(5):2001–2023, 2004. |
| | <!--* H. G. Feichtinger and F. Luef. "Wiener amalgam spaces for the Fundamental Identity of Gabor Analysis" Collect. Math. 57(Extra Volume (2006)):233—253, 2006.--> |
| | <!--* R. Aceska and H. G. Feichtinger. "Functions with variable bandwidth via time-frequency analysis tools" J. Math. Anal. Appl. 382(1), 2011.--> |
| | |
| | ==References== |
| | |
| | {{reflist}} |
| | |
| | == External links == |
| | *{{MathGenealogy|id=44893}} |
| | *[http://www.univie.ac.at/nuhag-php/home/fei.php Hans Georg Feichtinger's homepage] at University of Vienna |
| | *[http://www.univie.ac.at/nuhag-php/home/index.php NuHAG homepage] |
| | |
| | {{use dmy dates|date=May 2011}} |
| | |
| | {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> |
| | | NAME = Feichtinger, Hans Georg |
| | | ALTERNATIVE NAMES = |
| | | SHORT DESCRIPTION = mathematician |
| | | DATE OF BIRTH = 16 June 1951 |
| | | PLACE OF BIRTH = [[Wiener Neustadt]], [[Austria]] |
| | | DATE OF DEATH = |
| | | PLACE OF DEATH = |
| | }} |
| | {{DEFAULTSORT:Feichtinger, Hans Georg}} |
| | [[Category:1951 births]] |
| | [[Category:Living people]] |
| | [[Category:Austrian scientists]] |
| | [[Category:Austrian mathematicians]] |
| | [[Category:20th-century mathematicians]] |
Template:Infobox scientist
Hans Georg Feichtinger (born 16 June 1951) is an Austrian mathematician. He is Professor in the mathematical faculty of the University of
Vienna. He is editor-in-chief of the Journal of Fourier Analysis and Applications (JFAA) and associate editor to several other journals. He is one of the founders and head of the Numerical Harmonic Analysis Group (NuHAG) at University of Vienna. Today Feichtinger's main field of research is harmonic analysis with a focus on time-frequency analysis.
Biography
Hans Georg Feichtinger was born in Wiener Neustadt where he graduated from the Gymnasium and received the Matura "summa cum laude" in 1969. In the same year he started his studies in mathematics and physics. He finished his Ph.D. at the University of Vienna in 1974 under the supervision of Hans Reiter in 1974 with a doctoral thesis on Subalgebras of L1(G). Feichtinger attained professorship with the defense of his habilitation thesis on Banach convolution algebras of functions[1] in 1979. Feichtinger is author or co-author to roughly 200 scientific publications.
The University of Vienna being the center of his scientific life, Feichtinger still had several visiting positions across Europe and in the USA between 1980 and today, e.g. at the University of Maryland, College Park and the University of Connecticut, Storrs. He is married and the father of four children.[2]
The NuHAG (Numerical Harmonic Analysis Group)
In the late 1980s Hans Georg Feichtinger and Karlheinz Gröchenig conducted joint research on atomic decompositions. From 1990 on, Feichtinger investigated irregular sampling and computational harmonic analysis with Thomas Strohmer. These cooperations were the basis for founding the Numerical Harmonic Analysis Group (NuHAG) at the University of Vienna with Feichtinger as group leader. While the research project Experimental Signal Analysis is noted as the starting point of NuHAG [3] several earlier publications and projects are listed to be NuHAG related, the earliest dates back to 1986.[4] Over the years, NuHAG has become a group of international importance in the fields from abstract harmonic analysis to applied time-frequency analysis and currently hosts around 40 researchers (including PhD students).[5]
Dedication to the University of Vienna and the scientific community
Hans Georg Feichtinger is the editor-in-chief of the Journal of Fourier Analysis and Applications taking over from John J. Benedetto in the year 2000, and associate editor to the Journal of Approximation Theory (JAT), the Journal of Function spaces and Applications (JFSA) and Sampling Theory in Signal and Image Processing (STSIP). Furthermore, Feichtinger is the contact person for the European Union's student exchange programs ERASMUS and LEONARDO at the faculty of mathematics of the University of Vienna and is actively involved in workshops and conferences.[6] Throughout his career Hans G. Feichtinger has supervised 23 completed PhD theses, also today he is advising several students (as of June 2011).[7]
Scientific work
The scientific work of Hans Georg Feichtinger includes, but is not limited to results on function spaces, irregular sampling,
time-frequency analysis, Gabor analysis and frame theory. Some of his most notable contributions are listed below.
In the early 1980s, Feichtinger introduced modulation spaces, a family of function spacesdefined by the behavior of the short-time Fourier transform with respect to a test function from the Schwartz space. They have become the standard spaces in time-frequency analysis. Also, while the concept of function spaces treating local and global behavior separately was already known earlier, Wiener amalgam spaces were introduced by Feichtinger in 1980, also his publications have contributed to the acknowledgment of amalgam spaces as a useful tool in various mathematical fields.
Around 1990 the joint research with Karlheinz Gröchenig lead to a series of papers, which is today referred to as coorbit theory. The theory provides a unified framework for different important transforms, e.g. the wavelet transform and the short-time Fourier transform.
Feichtinger also proposed the use of Banach Gelfand triples, especially the Banach Gelfand triple that has proven very useful, e.g. in time-frequency analysis.
Feichtinger's conjecture
Feichtinger once raised the question, whether
- Every bounded frame can be written as a finite union of Riesz basic sequences.
This question is not only an important open problem in frame theory but is equivalent to some famous open problems in analysis. The statement above is now widely referred to as Feichtinger's conjecture, a term first used by Pete G. Casazza.
Proofs are known for certain special cases since 2005.[8][9] In 2013 the conjecture has been proved by Adam Marcus, Daniel A Spielman and Nikhil Srivastava.[10]
Selected publications
Hans Georg Feichtinger has published approximately 200 scientific articles,[11] a selection of which is presented below (in chronological order):
- H. G. Feichtinger. "On a new Segal algebra" Monatsh. Math. 92:269–289, 1981.
- H. G. Feichtinger. "Banach convolution algebras of Wiener type" in Proc. Conf. on Functions, Series, Operators, Budapest 1980, North-Holland, Amsterdam, 1983.
- H. G. Feichtinger and K. Gröchenig. "A unified approach to atomic decompositions via integrable group representations" Lect. Notes in Math. 1302:52—73, 1988.
- H. G. Feichtinger and K. Gröchenig. "Gabor wavelets and the Heisenberg group: Gabor expansions and short time Fourier transform from the group theoretical point of view" in Wavelets :a tutorial in theory and applications, Academic Press, Boston, 1992.
- H. G. Feichtinger and K. Gröchenig. "Theory and practice of irregular sampling" in "Wavelets: Mathematics and Applications ", CRC Press, Studies in Advanced Mathematics:305—363, 1994.
- H. G. Feichtinger and K. Gröchenig. "Gabor frames and time-frequency analysis of distributions" J. Funct. Anal. 146(2):464–495, 1997.
- H. Bölcskei, F. Hlawatsch and H. G. Feichtinger. "Frame-theoretic analysis of oversampled filter banks" IEEE Trans. Signal Processing 46(12):3256–3268, 1998.
- H. G. Feichtinger and T. Strohmer (editors). "Gabor Analysis and Algorithms. Theory and Applications.", Birkhäuser, Boston, 1998.
- H. G. Feichtinger and T. Strohmer (editors). "Advances in Gabor Analysis", Birkhäuser, Basel, 2003.
- H. G. Feichtinger and N. Kaiblinger. Varying the time-frequency lattice of Gabor frames. Trans. Amer. Math. Soc., 356(5):2001–2023, 2004.
References
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External links
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Template:Persondata
- ↑ [1], Universitätsbibliothek Wien
- ↑ [2], Hans Georg Feichtinger's Homepage
- ↑ [3], The 'Experimental Signal Analysis' project at NuHAG
- ↑ [4], NuHAG research page
- ↑ [5], NuHAG member page
- ↑ [6], NuHAG event database
- ↑ [7], Completed PhD studies under Hans Georg Feichtinger at Math. Genealogy
- ↑ Frames and the Feichtinger Conjecture by Peter G. Casazza, Ole Christensen, Alexander M. Lindner and Roman Vershynin
- ↑ The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates by Marcin Bownik and Darrin Speegle
- ↑ Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem by Adam Marcus, Daniel A Spielman and Nikhil Srivastava
- ↑ [8], NuHAG BIBTEX database