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- Karlheinz Gröchenig

Mathematics

Austria

2023

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
62
Citations
16,969
196
World Ranking
330
National Ranking
5

2023 - Research.com Mathematics in Austria Leader Award

2022 - Research.com Mathematics in Austria Leader Award

- Mathematical analysis
- Algebra
- Hilbert space

His scientific interests lie mostly in Modulation space, Mathematical analysis, Pure mathematics, Algorithm and Time–frequency analysis. His Modulation space study combines topics in areas such as Discrete mathematics, Operator theory and Bounded function. As a part of the same scientific family, Karlheinz Gröchenig mostly works in the field of Mathematical analysis, focusing on Function and, on occasion, Convolution and Kernel method.

Karlheinz Gröchenig interconnects Class, Besov space and Wavelet in the investigation of issues within Pure mathematics. His biological study spans a wide range of topics, including Frame and Hilbert space. Karlheinz Gröchenig usually deals with Time–frequency analysis and limits it to topics linked to Harmonic analysis and Algebra over a field and Theoretical physics.

- Foundations of Time-Frequency Analysis (1993 citations)
- Banach spaces related to integrable group representations and their atomic decompositions, I (671 citations)
- Banach spaces related to integrable group representations and their atomic decompositions, I (671 citations)

Karlheinz Gröchenig spends much of his time researching Pure mathematics, Mathematical analysis, Modulation space, Discrete mathematics and Combinatorics. The various areas that Karlheinz Gröchenig examines in his Pure mathematics study include Class, Bounded function, Group and Time–frequency analysis. His research in Mathematical analysis is mostly concerned with Fourier transform.

His Modulation space study results in a more complete grasp of Algebra. His studies deal with areas such as Convolution and Operator theory as well as Algebra. He has researched Combinatorics in several fields, including Lambda, Invariant and Entire function.

- Pure mathematics (36.29%)
- Mathematical analysis (25.00%)
- Modulation space (18.15%)

- Pure mathematics (36.29%)
- Combinatorics (11.69%)
- Fourier transform (10.89%)

His main research concerns Pure mathematics, Combinatorics, Fourier transform, Hilbert space and Modulation space. Pure mathematics connects with themes related to Time–frequency analysis in his study. His Combinatorics research is multidisciplinary, relying on both Lambda, Gaussian and Invariant.

His research in Fourier transform intersects with topics in Zero, Bessel function, Exponential function and Zero set. The Hilbert space study which covers Linear subspace that intersects with Bergman space, Hardy space, Analytic function, Variable and Operator norm. His Modulation space research includes elements of Space, Embedding, Uniqueness and Initial value problem.

- Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions (30 citations)
- Harmonic Analysis in Phase Space and Finite Weyl-Heisenberg Ensembles. (13 citations)
- Orthonormal bases in the orbit of square-integrable representations of nilpotent Lie groups (9 citations)

- Mathematical analysis
- Algebra
- Hilbert space

His primary scientific interests are in Fourier transform, Pure mathematics, Zero set, Exponential function and Short-time Fourier transform. His study in the field of Fourier analysis also crosses realms of Stability. His studies in Pure mathematics integrate themes in fields like Fock space, Kernel and Interpolation.

His Zero set research is multidisciplinary, incorporating elements of Zero and Bessel function.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Foundations of Time-Frequency Analysis

Karlheinz Gröchenig.

**(2000)**

3433 Citations

Banach spaces related to integrable group representations and their atomic decompositions, I

Hans G Feichtinger;Hans G Feichtinger;K.H Gröchenig;K.H Gröchenig.

Journal of Functional Analysis **(1989)**

1104 Citations

Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

Akram Aldroubi;Karlheinz Gröchenig.

Siam Review **(2001)**

865 Citations

Describing functions: Atomic decompositions versus frames

Karlheinz Gröchenig.

Monatshefte für Mathematik **(1991)**

614 Citations

Theory and practice of irregular sampling

Hans G. Feichtinger;Karlheinz Gröchenig.

**(2021)**

451 Citations

Banach spaces related to integrable group representations and their atomic decompositions. Part II

Hans G. Feichtinger;K. H. Gröchenig.

Monatshefte für Mathematik **(1989)**

431 Citations

Multiresolution analysis. Haar bases, and self-similar tilings of R/sup n/

K. Grochenig;W.R. Madych.

IEEE Transactions on Information Theory **(1992)**

429 Citations

Efficient numerical methods in non-uniform sampling theory

Hans G. Feichtinger;Karlheinz Gröchenig;Thomas Strohmer.

Numerische Mathematik **(1995)**

369 Citations

A unified approach to atomic decompositions via integrable group representations

Hans G. Feichtinger;Karlheinz Gröchenig.

**(1988)**

330 Citations

Reconstruction algorithms in irregular sampling

Karlheinz Gröchenig.

Mathematics of Computation **(1992)**

317 Citations

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