6 papers · 1 filter
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…
Ramanujan sums in signal recovery and uncertainty principle inequalities
Sahil Kalra, Niraj K. Shukla
This paper explores the perfect reconstruction property of filter banks based on Ramanujan sums and their applications in signal recovery. Originally introduced by Srinivasa Ramanu…
Cyclic frames in finite-dimensional Hilbert spaces
Ole Christensen, Navneet Redhu, Niraj K. Shukla
Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dy…
An Application of the supremum cosine angle between multiplication invariant spaces in $L^2(X; \mc H)$
Sudipta Sarkar, Sahil Kalra, Niraj K. Shukla
In this article, we describe the supremum cosine angle between two multiplication invariant (MI) spaces and its connection with the closedness of the sum of those spaces. The resul…
Microlocal analysis and characterization of Sobolev wavefront sets using shearlets
Bin Han, Swaraj Paul, Niraj K. Shukla
Sobolev wavefront sets and -microlocal spaces play a key role in describing and analyzing the singularities of distributions in microlocal analysis and solutions of partial diff…
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…