arXiv subjects

Saikat Mukherjee

Publications and source records attributed to Saikat Mukherjee.

21 records · Page 2Linked to original sources

arXiv2019

Characterizations of woven frames

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $σ\subset I$, $\{f_i\}_{i \in σ} \cup \{g_i\}_{i \in σ^c}$ forms a frame for $\mathcal H$ with the universal bounds $A, B$. This article provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.

math.FA↗

arXiv2018

Perturbations on K-fusion frames

K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed.

math.FA↗

arXiv2012

Characterization of Differentiable Copulas

This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spearman's rho and Kendall's tau for our new Fourier copulas which are asymmetric are introduced. Furthermore, an approximation method is discussed in order to optimize Spearman's rho and the corresponding Kendall's tau.

stat.ME↗