"The volume is based on the Sobolev-Schwarz concept of generalized functions. It presents general theory including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner, Poisson integral transforms and also operational calculus. Traditional material is supplemented by the theory…
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quant…
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quant…
This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson's type before turning to q-difference equations. The existence and unique…
1. Preliminaries. 1.1. The spaces Lp and Lp(p). 1.2. Special functions of the hypergeometric type. 1.3. Fourier's, Mellin's and Laplace's transforms. 1.4. General Mellin convolution type integral transforms. 1.5. Notion of the index transforms -- 2. The Kontorovich-Lebedev trans…
This book deals with the theory and some applications of integral transforms that involve integration with respect to an index or parameter of a special function of hypergeometric type as the kernel (index transforms). The basic index transforms are considered, such as the Konto…
