Gröchenig, Karlheinz
Overview
Works:  12 works in 39 publications in 1 language and 683 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  TK5102.9, 621.3822 
Publication Timeline
.
Most widely held works by
Karlheinz Gröchenig
Foundations of timefrequency analysis : with 15 figures by
Karlheinz Gröchenig(
Book
)
17 editions published between 2001 and 2014 in English and held by 354 WorldCat member libraries worldwide
"Timefrequency analysis is a source of ideas and applications in modern harmonic analysis. The history of timefrequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years timefrequency analysis has been pursued mainly in engineering, but recently  with the development of wavelet theory  it has emerged as a thriving field of applied mathematics."
17 editions published between 2001 and 2014 in English and held by 354 WorldCat member libraries worldwide
"Timefrequency analysis is a source of ideas and applications in modern harmonic analysis. The history of timefrequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years timefrequency analysis has been pursued mainly in engineering, but recently  with the development of wavelet theory  it has emerged as a thriving field of applied mathematics."
Operatorrelated function theory and timefrequency analysis : the Abel Symposium 2012 by
Karlheinz Gröchenig(
Book
)
10 editions published between 2015 and 2016 in English and held by 13 WorldCat member libraries worldwide
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operatorrelated function theory and timefrequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewisesmooth functions; ℗ℓBernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by worldleading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing
10 editions published between 2015 and 2016 in English and held by 13 WorldCat member libraries worldwide
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operatorrelated function theory and timefrequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewisesmooth functions; ℗ℓBernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by worldleading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing
Implementation of discretized Gabor frames and their duals by
Tobias Kloos(
Book
)
1 edition published in 2015 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 4 WorldCat member libraries worldwide
Optimal adaptive computations in the Jaffard algebra and localized frames by
Stephan Dahlke(
Book
)
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
A new approach to interpolating scaling functions by
Stephan Dahlke(
Book
)
2 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
Biorthogonal box spline wavelet bases by
Stephan Dahlke(
Book
)
1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide
Note on Bsplines, wavelet scaling functions, and Gabor frames(
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and timeshift and frequencyshift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3,0... and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b = 2, 3,... and a > 0. We give an example for our result for the case that g = B <sub>1</sub>, the triangle function supported by [  1, 1], by showing pictures of the canonical dual corresponding to (g, a, b) where ab = 1/4 and b crosses the lines N = 2, 3
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and timeshift and frequencyshift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3,0... and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b = 2, 3,... and a > 0. We give an example for our result for the case that g = B <sub>1</sub>, the triangle function supported by [  1, 1], by showing pictures of the canonical dual corresponding to (g, a, b) where ab = 1/4 and b crosses the lines N = 2, 3
Letter to the editor: A new criterion for Gabor frames(
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
We give a new criterion for the invertibility of the Gabor frame operator in the irrational case. It is sufficient to verify the invertibility of a single (infinite) matrix
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
We give a new criterion for the invertibility of the Gabor frame operator in the irrational case. It is sufficient to verify the invertibility of a single (infinite) matrix
Localization of frames by Elena Cordero(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Compactness criteria in function spaces by
M Dörfler(
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
Four Short Courses on Harmonic Analysis(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
Multivariate Wavelet Representations and Approximations(
)
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
The following work has been completed: The recovery of irregularly samples bandlimited functions via tempered splines. Band limited functions can be recovered from their values on certain irregularly distributed discrete sampling sets as the limits of the piecewise polynomial spline interpolants when the order of the splines goes to infinity. This significant extension of the classical case when the sampling set is a lattice which was considered by L. Collatz, W. Quade, I.J. Schoenberg, and others. Orthogonality criteria for compactly supported scaling functions. The question of whether the integer translates of the scaling function constructed from a prescribed scaling sequency in the standard way are mutually orthogonal is quite subtle. The various conditions and the supporting arguments which are currently in the literature are very complicated
1 edition published in 1994 in English and held by 0 WorldCat member libraries worldwide
The following work has been completed: The recovery of irregularly samples bandlimited functions via tempered splines. Band limited functions can be recovered from their values on certain irregularly distributed discrete sampling sets as the limits of the piecewise polynomial spline interpolants when the order of the splines goes to infinity. This significant extension of the classical case when the sampling set is a lattice which was considered by L. Collatz, W. Quade, I.J. Schoenberg, and others. Orthogonality criteria for compactly supported scaling functions. The question of whether the integer translates of the scaling function constructed from a prescribed scaling sequency in the standard way are mutually orthogonal is quite subtle. The various conditions and the supporting arguments which are currently in the literature are very complicated
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Approximation theory Computer engineering Computer vision Differentiable dynamical systems Differential equations, Partial Dynamics Engineering Ergodic theory Fourier analysis Frequency spectra Image processing Mathematics Signal processing Signal processingMathematics Timeseries analysis Topological groups
Alternative Names
Gröchenig, K.
Gröchenig, Karlheinz
Karlheinz Gröchenig austerriksk matematikar
Karlheinz Gröchenig Austrian mathematician
Karlheinz Gröchenig matemático austríaco
Karlheinz Gröchenig österreichischer Mathematiker
Karlheinz Gröchenig österrikisk matematiker
Karlheinz Gröchenig østerriksk matematiker
Karlheinz Gröchenig østrigsk matematiker
Karlheinz Gröchenig wiskundige uit Oostenrijk
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