S. G. Mikhlin – författare

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm''s equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz''s method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.