Related papers: Analysis in $R^{1,1}$ or the Principal Function Th…

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied,…

The $k$-Cauchy-Fueter complex, $k=0,1,\ldots$, in quaternionic analysis are the counterpart of the Dolbeault complex in the theory of several complex variables. In this paper, we construct explicitly boundary complexes of these complexes on…

Using properties of the Riemann zeta-function we propose two new large classes of evaluated series. Incidentally the first class represents integrals as generalized average on very nonuniform sequences. The second class contains inter alia…

In the search for hypercomplex analytic functions on the half-plane, we review the construction of induced representations of the group G=SL(2,R). Firstly we note that G-action on the homogeneous space G/H, where H is any one-dimensional…

We introduce a notion of complexity for systems of linear forms, called sequential Cauchy-Schwarz complexity, which is parametrized by two positive integers $k,\ell$ and refines the notion of Cauchy-Schwarz complexity introduced by Green…

We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…

There exist many explicit evaluations of Dirichlet series. Most of them are constructed via the same approach: by taking products or powers of Dirichlet series with a known Euler product representation. In this paper we derive a result of a…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…

This paper focuses on the development of harmonic and Clifford analysis techniques in the context of some conformally flat manifolds that arise from factoring out a simply-connected domain from $R^n$ by special arithmetic subgroups of the…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

The concept of monogenic functions over real alternative $\ast$-algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hypercomplex analysis, including quaternionic, octonionic, and…

We evaluate in closed form several series involving products of Cauchy numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic, and central binomial). Similar results are obtained with series involving Stirling numbers of…

In these notes we define and study the Shahidi local coefficients matrix associated with a genuine principal series representation I({\sigma}) of an n-fold cover of p-adic SL(2,F) and an additive character {\psi}. The conjugacy class of…

In this paper, we deal with the convolution series that are a far reaching generalization of the conventional power series and the power series with the fractional exponents including the Mittag-Leffler type functions. Special attention is…

We find the complete branching law for the restriction of certain unitary representations of $O(1,n+1)$ to the subgroups $O(1,m+1)\times O(n-m)$, $0\leq m\leq n$. The unitary representations we consider belong either to the unitary…

In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$…

Recently, Shehata et al. [37] introduced the $_{r+1}R_{s,k}(B,C,z)$ matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence…

In this paper, we introduce a pair of multiplication-like operations, $L_0$ and $L_1$, which derive $k$-regular functions from $(k+1)$-regular functions. The investigation of the inverse problem naturally leads to a deeper study of the…

The character of the principal series of representations of SL(n,R) is evaluated by using Gel'fand and Naimark's definition of character. This representation is realized in the space of functions defined on the right coset space of SL(n,R)…