Ramanujan expansions of arithmetic functions of several variables

Fourier Expansions of Functions with Bounded Variation of Several Variables

In the first part of the paper we establish the pointwise convergence as t → +∞ for convolution operators ∫ Rd tdK (ty)φ(x− y)dy under the assumptions that φ(y) has integrable derivatives up to an order α and that |K(y)| ≤ c (1 + |y|)−β with α+β > d. We also estimate the Hausdorff dimension of the set where divergence may occur. In particular, when the kernel is the Fourier transform of a bound...

Mean-value Theorems for Multiplicative Arithmetic Functions of Several Variables

Let f : Nn → C be an arithmetic function of n variables, where n ≥ 2. We study the mean-value M(f) of f that is defined to be lim x1,...,xn→∞ 1 x1 · · ·xn ∑ m1≤x1, ... , mn≤xn f(m1, . . . , mn), if this limit exists. We first generalize the Wintner theorem and then consider the multiplicative case by expressing the mean-value as an infinite product over all prime numbers. In addition, we study ...

Summability of orthogonal expansions of several variables

Approximately generalized additive functions in several variables

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

Functions of Several Noncommuting Variables

The notions of nonsingularity, resolvent set, and spectrum, and the corresponding analytic functional calculus for n-tuples of elements of a commutative Banach algebra provide some of the deepest and most potent tools of modern analysis. A point of view one can adopt regarding this theory is as follows: The class of algebras (9(U)9 for U a domain in C9 provides a relatively small, well-understo...