Related papers: Hermitian Quaternion Toeplitz Matrices by Quaterni…
This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there…
We construct new integral representations for transformations of the ordinary generating function for a sequence, $\langle f_n \rangle$, into the form of a generating function that enumerates the corresponding "square series" generating…
We consider the class of non-Hermitian operators represented by infinite tridiagonal matrices, selfadjoint in an indefinite inner product space with one negative square. We approximate them with their finite truncations. Both infinite and…
Since their introduction by Andrews, generalized Frobenius partitions have interested a number of authors, many of whom have worked out explicit formulas for their generating functions in specific cases. This has uncovered interesting…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
Within the framework of the theory of the column and row determinants, we obtain determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field. Using the obtained determinantal representations of…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We consider the singular linear statistic of the Laguerre unitary ensemble consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz…
We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain…
We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and…
The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered,…
Let $L/F$ be a quadratic extension of totally real number fields. For any prime $p$ unramified in $L$, we construct a $p$-adic $L$-function interpolating the central values of the twisted triple product $L$-functions attached to a…
From the realization of $q-$oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szeg\H{o} polynomials as well as…
We introduce the notion of a confluent Vandermonde matrix with quaternion entries and discuss its connection with Lagrange-Hermite interpolation over quaternions. Further results include the formula for the rank of a confluent Vandermonde…
In this paper, we study the eigenvalues of the matrices $T_n(a)+\gamma E_{n,1,1}$ where $T_n(a)$ is the Toeplitz matrix with generating symbol $a(t)=t-t^{-1}$, $E_{n,1,1}$ is the $n\times n$ matrix whose upper left component is $1$ and the…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…