We determine the subspaces of solutions of the systems of Laplace and heat-conduction differential equations isometric to the corresponding spaces of real functions defined on the set of real numbers.
In weighted Orlicz-type spaces S-p,S- (mu) with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the space ...Daha fazlası
In this paper, we study the uniform convergence ofp-Bieberbach polynomials in regions with a finite number of both interior and exterior zero angles at the boundary.