9 papers
Characterization and Construction of Pairwise Orthogonal Parseval Frames with Applications to Sampling
Navneet Redhu, Anupam Gumber, Hartmut Führ +1
In this paper, we provide a characterization of pairwise orthogonal frames with generalized translation-invariant (GTI) structures, based on the unconditional convergence property…
Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces
Anupam Gumber, Nimit Rana, Joachim Toft +1
We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend we…
The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators
Markus Faulhuber, Anupam Gumber, Irina Shafkulovska
We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interest…
Fourier characterizations of Pilipovic spaces
Joachim Toft, Anupam Gumber
Let be a function or distribution on $\rr d$. We show that belongs to a certain Pilipovi{ć} space, if and only if and suitable partial fractional Fourier transforms of…
Completeness of Sets of Shifts in Invariant Banach Spaces of Tempered Distributions via Tauberian conditions
Hans G. Feichtinger, Anupam Gumber
The main result of this paper is a far reaching generalization of the completeness result given by V.~Katsnelson in a recent paper [35]. Instead of just using a collection of dilat…
Completeness of shifted dilates in invariant Banach spaces of tempered distributions
Hans G. Feichtinger, Anupam Gumber
We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated v…
Translation and modulation invariant Hilbert spaces
Joachim Toft, Anupam Gumber, Ramesh Manna +1
We show that for any Hilbert space of distributions on which is translation and modulation invariant, is equal to , with the same norm apart from…
Orthogonality and duality of frames over locally compact abelian groups
Anupam Gumber, Niraj K. Shukla
Motivated by the recent work of Bownik and Ross \cite{BR}, and Jakobsen and Lemvig \cite{JL}, this article generalizes latest results on reproducing formulas for generalized transl…
Orthonormal Wavelet System in
Anupam Gumber, Niraj K. Shukla
Using the group theoretic approach based on the set of digits, we first investigate a finite collection of functions in that satisfies some localization…