Search results for ""Author Sorin G Gal""
World Scientific Publishing Co Pte Ltd Approximation By Complex Bernstein And
Book SynopsisThe monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.Table of ContentsBernstein-Type Operators of One Complex Variable: Auxiliary Results in Complex Analysis; Bernstein Polynomials; Iterates of Bernstein Polynomials; Generalized Voronovskaja Theorems for Bernstein Polynomials; Butzer's Linear Combination of Bernstein Polynomials; q-Bernstein Polynomials; Bernstein-Stancu Polynomials; Bernstein-Kantorovich Type Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Balazs-Szabados Operators; Bibliographical Notes and Open Problems; Bernstein-Type Operators of Several Complex Variables: Introduction; Bernstein Polynomials; Favard-Szasz-Mirakjan Operators; Baskakov Operators; Bibliographical Notes and Open Problems; Complex Convolutions: Linear Polynomial Convolutions; Linear Non-Polynomial Convolutions; Nonlinear Complex Convolutions; Bibliographical Notes and Open Problems; Appendices: Related Topics: Bernstein Polynomials of Quaternion Variable; Approximation of Vector-Valued Functions; Strong Approximation by Complex Taylor Series; Bibliographical Notes and Open Problems.
£95.40
World Scientific Publishing Co Pte Ltd Evolution Equations With A Complex Spatial
Book SynopsisThis book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations.The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought.For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.
£67.45
