Related papers: $({\mathrm R},{\mathcal B})$-Multidimensional-almo…

The like-Lebesgue integral of real-valued measurable functions (abbreviated as \textit{RVM-MI})is the most complete and appropriate integration Theory. Integrals are also defined in abstract spaces since Pettis (1938). In particular,…

The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…

The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…

We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal…

In this paper, we introduce the concept of $S^{2}$-weighted pseudo almost automorphy for stochastic processes. We study the existence and uniqueness of square-mean weighted pseudo almost automorphic solutions for the semilinear stochastic…

In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…

We show that functions in $GSBV^p$ in three-dimensional space with small variation in $2$ of $3$ directions are close to a function of one variable outside an exceptional set. Bounds on the volume and the perimeter in these two directions…

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a…

Let $G$ be a split simply-connected group of type $D$ or $E$. The minimal automorphic representation $\Pi$ of $G(\mathbb A)$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$. In this paper we write…

For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded…

In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leq q\leq \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, we…

The main aim of this paper is to introduce and analyze the notions of subspace almost periodicity and subspace weak almost periodicity for $C$-distribution semigroups and $C$-distribution cosine functions in Banach spaces. We continue our…

For a class of $\mathbb{R}^d$-ations and $\mathbb{Z}^d$-actions on the $n$-dimensional torus $\mathbb{T}^n$, we characterize their unique ergodicity and establish a theorem of Weyl type. This result allows us to establish an isomorphism…

We present a new approach to define a suitable integral for functions with values in quasi-Banach spaces. The integrals of Bochner and Riemann have deficiencies in the non-locally convex setting. The study of an integral for $p$-Banach…

We realize the relative discrete series of a weighted $L^2$-space on a bounded symmetric doamin as kernels of invariant Cauchy-Riemann operator, and thus as the spaces of nearly holomorphic functions.

In our previous paper q-alg/9605011 we proposed several algebraic methods for constructing new solutions to the bispectral problem. In the present note the corresponding eigenfunctions are explicitly constructed as multiple Laplace…

In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its…

Inspired by Morrey's Problem (on rank-one convex functionals) and the Burkholder integrals (of his martingale theory) we find that the Burkholder functionals $B_p$, $p \ge 2$, are quasiconcave, when tested on deformations of identity $f\in…

In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…