相关论文: The Cauchy Operator for Basic Hypergeometric Serie…

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…

We derive two generalizations of Gasper's transformation formula for basic hypergeometric series. Using these generalized formulas, we give explicit expressions for the coefficients of three-term relations for the basic hypergeometric…

We study the Cauchy problem for one-dimensional dispersive equations posed on $\mathbb{R} $, under the hypotheses that the dispersive operator behaves, for high frequencies, as a Fourier multiplier by $ i |\xi|^\alpha \xi $ with $ 1 \le…

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case…

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric…

We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert space of the solution to the Cauchy problem associated to Gauss-Laguerre invariant Markov semigroups that we introduce. Their generators turn out to be…

The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed,…

In this paper, we establish the two weight commutator of Calder\'on--Zygmund operators in the sense of Coifman--Weiss on spaces of homogeneous type, by studying the weighted Hardy and BMO space for $A_2$ weight and by proving the sparse…

Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a novel bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, involving…

In a recent paper (2024) Camacho, C\'{a}novas, Mart\'{\i}nez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility…

We consider the Cauchy problem for one-dimensional dispersive equations with a general nonlinearity in the periodic setting. Our main hypotheses are both that the dispersive operator behaves for high frequencies as a Fourier multiplier by $…

By studying Cameron's operator in terms of determinants, two kinds of "integer" sequences of incomplete numbers were introduced. One was the sequence of restricted numbers, including $s$-step Fibonacci sequences. Another was the sequence of…

In this paper, we give Poisson and Cauchy representation theorems in Hardy-Orlicz spaces on the upper complex half-plane. We use these theorems for the construction of dual spaces of certain Hardy-Orlicz spaces and also for the…

In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…

Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised 8phi7 series. In this paper we use this fact to derive various basic hypergeometric and…

We study the Cauchy problem for effectively hyperbolic operators $P$ with principal symbol $p(t, x,\tau,\xi)$ having triple characteristics on $t = 0$. Under a condition (E) we show that such operators are strongly hyperbolic, that is the…

In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy-Riemann operator acting on octonions. In particular, we establish a discrete octonionic version…

A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…

We derive double-product representations of nonterminating basic hypergeometric series using diagonalization, a method introduced by Theo William Chaundy in 1943. We refer to this result as the $q$-Chaundy theorem and several limiting $q\to…

Cauchy problem for an abstract hyperbolic equation with the Lipschitz continuous operator is considered in the Hilbert space. The operator corresponding to the elliptic part of the equation is a sum of operators…