13 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…
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…
Subspace Dual and orthogonal frames\\ by action of an abelian group
Sudipta Sarka, Niraj K. Shukla
In this article, we discuss subspace duals of a frame of translates by an action of a closed abelian subgroup of a locally compact group These subspace duals are…
A characterization of MG Dual frames using infimum cosine angle
Sudipta Sarkar, Niraj K. Shukla
This article discusses the construction of dual frames and their uniqueness for the multiplication generated frames on , where is a -finite measure. A ne…
Reproducing formulas associated to translation generated systems on Nilpotent Lie Groups
Sudipta Sarkar, Niraj K. Shukla
Let be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results…
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…
Characterizations of Extra-invariant spaces under the left translations on a Lie group
Sudipta Sarkar, Niraj K. Shukla
In the context of a connected, simply connected, nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invar…
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…
Semi-orthogonal Parseval wavelets associated to GMRAs on local fields of positive characteristics
Niraj K. Shukla, Saurabh Chandra Maury, Shiva Mittal
In this article we establish theory of semi-orthogonal Parseval wavelets associated to generalized multiresolution analysis (GMRA) for the local field of positive characteristics (…
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…
Super-wavelets on local fields of positive characteristic
Niraj K. Shukla, Saurabh C. Maury
The concept of super-wavelet was introduced by Balan, and Han and Larson over the field of real numbers which has many applications not only in engineering branches but also in dif…