Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 11
Submit an article Journal homepage
188
Views
28
CrossRef citations to date
0
Altmetric
Original Articles

Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group

Luís Daniel Abreu Department of Mathematics, CMUC, University of Coimbra, School of Science and Technology (FCTUC), 3001-454 Coimbra, PortugalCorrespondence[email protected]
&
Karlheinz Gröchenig Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria
Pages 1981-1997 | Accepted 11 Apr 2011, Published online: 14 Sep 2011

Citations (28)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (1)

Luís V. Pessoa. (2015) On the structure of polyharmonic Bergman-type spaces over the unit disk. Complex Variables and Elliptic Equations 60:12, pages 1668-1684.
Read now

Articles from other publishers (27)

Sorin G. Gal & Irene Sabadini. (2023) Density of Complex and Quaternionic Polyanalytic Polynomials in Polyanalytic Fock Spaces. Complex Analysis and Operator Theory 18:1.
Crossref
Nuno Costa Dias, João Nuno Prata & Nenad Teofanov. (2023) Gabor products and a phase space approach to nonlinear analysis. Analysis and Applications 21:06, pages 1417-1446.
Crossref
Sorin G. Gal & Irene Sabadini. (2022) Approximation by Convolution Polyanalytic Operators in the Complex and Quaternionic Compact Unit Balls. Computational Methods and Function Theory 23:1, pages 101-123.
Crossref
Helge Knutsen. (2023) A fractal uncertainty principle for the short-time Fourier transform and Gabor multipliers. Applied and Computational Harmonic Analysis 62, pages 365-389.
Crossref
Michael Speckbacher. (2022) Sampling Trajectories for the Short-Time Fourier Transform. Journal of Fourier Analysis and Applications 28:6.
Crossref
Luís Daniel Abreu & Michael Speckbacher. (2021) Donoho-Logan large sieve principles for modulation and polyanalytic Fock spaces. Bulletin des Sciences Mathématiques 171, pages 103032.
Crossref
Philippe Jaming & Michael Speckbacher. (2020) Planar Sampling Sets for the Short-Time Fourier Transform. Constructive Approximation 53:3, pages 479-502.
Crossref
Johannes Keller & Franz Luef. (2021) Polyanalytic Toeplitz Operators: Isomorphisms, Symbolic Calculus and Approximation of Weyl Operators. Journal of Fourier Analysis and Applications 27:3.
Crossref
S. Twareque Ali, Zouhaïr Mouayn & Khalid Ahbli. (2020) Nonlinear Coherent States Associated with a Measure on the Positive Real Half Line. Complex Analysis and Operator Theory 14:1.
Crossref
Luis Daniel Abreu & Michael Speckbacher. (2019) Deterministic guarantees for L 1 -reconstruction: A large sieve approach with geometric flexibility . Deterministic guarantees for L 1 -reconstruction: A large sieve approach with geometric flexibility .
Olivia Constantin. (2019) Intermediate Hankel operators on the Fock space. Journal of Mathematical Analysis and Applications 471:1-2, pages 687-691.
Crossref
Zouhaïr Mouayn. (2017) Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator. Analysis and Mathematical Physics 9:1, pages 367-383.
Crossref
Luís Daniel Abreu, Karlheinz Gröchenig & José Luis Romero. (2019) Harmonic Analysis in Phase Space and Finite Weyl–Heisenberg Ensembles. Journal of Statistical Physics 174:5, pages 1104-1136.
Crossref
Paula Cerejeiras, Stefan Hartmann & Heikki Orelma. (2018) Structural Results for Quaternionic Gabor Frames. Advances in Applied Clifford Algebras 28:5.
Crossref
Nathanaël Perraudin, Nicki Holighaus, Peter L. Søndergaard & Peter Balazs. (2018) Designing Gabor windows using convex optimization. Applied Mathematics and Computation 330, pages 266-287.
Crossref
J. S. Ben-Benjamin, L. Cohen, N. C. Dias, P. Loughlin & J. N. Prata. (2018) What is the Wigner Function Closest to a Given Square Integrable Function?. SIAM Journal on Mathematical Analysis 50:5, pages 5161-5197.
Crossref
Luis Daniel Abreu & Michael Speckbacher. (2017) A planar large sieve and sparsity of time-frequency representations. A planar large sieve and sparsity of time-frequency representations.
Saifallah Ghobber. (2017) Some results on wavelet scalograms. International Journal of Wavelets, Multiresolution and Information Processing 15:03, pages 1750019.
Crossref
Luís V. Pessoa & Ana Moura Santos. (2017) Polyharmonic Bergman spaces and Bargmann type transforms. Journal of Mathematical Analysis and Applications 449:1, pages 619-641.
Crossref
Maurice A. de Gosson. (2017) The canonical group of transformations of a Weyl–Heisenberg frame; applications to Gaussian and Hermitian frames. Journal of Geometry and Physics 114, pages 375-383.
Crossref
Luís Daniel Abreu. (2016) Superframes and Polyanalytic Wavelets. Journal of Fourier Analysis and Applications 23:1, pages 1-20.
Crossref
D. Barbieri & G. Citti. (2015) Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group. Analysis and Applications 13:03, pages 331-346.
Crossref
Yingxiong Fu, Luoqing Li, Uwe Kaehler & Paula Cerejeiras. (2014) On the Fock space of metaanalytic functions. Journal of Mathematical Analysis and Applications 414:1, pages 176-187.
Crossref
Monika Dörfler & José Luis Romero. (2014) Frames Adapted to a Phase-Space Cover. Constructive Approximation 39:3, pages 445-484.
Crossref
Luis Daniel Abreu & Hans G. Feichtinger. 2014. Harmonic and Complex Analysis and its Applications. Harmonic and Complex Analysis and its Applications 1 38 .
Luis Daniel Abreu. (2012) Super-Wavelets Versus Poly-Bergman Spaces. Integral Equations and Operator Theory 73:2, pages 177-193.
Crossref
Helge Knutsen. (2022) A Fractal Uncertainty Principle for the Short-Time Fourier Transform and Gabor Multipliers. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.