Approximation of functions of several variables by multidimensional $S$-fractions with independent 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.

Reducibility of Rational Fractions in Several Variables

We prove a analogous of Stein theorem for rational fractions in several variables: we bound the number of reducible fibers by a formula depending on the degree of the fraction.

Approximation of smooth periodic functions in several 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...

Best Approximation of Monomials in Several Variables

For a monomial x in d variables, the problem of best approximation to x by polynomials of lower degrees is studied on the unit sphere, the unit ball and the standard simplex. For the uniform norm we discuss what is known in d = 2, for which complete solutions are known, and in d ≥ 3 for which only a few cases have been successfully solved. For the L norm, we present the complete solution, inclu...