Abstract
BASIC CONCEPTS AND FORMULATIONS - Concepts in Linear Algebra - Point Latices - Some Functional Spaces - Generalized Derivatives and Pdm@ve Functions - Densi@ of Fin4e Fundons - P@ncipal Embedding Theorems for We@hted Spaces - Fundons of a Discrete kgument - Generalized Functions - Fou@er Transformabon of Generalized Functions - Periodic Functions and Generalized Functions - Generalized Spherical Harmonics - POLYHARMONIC EQUATION - Green's Formula - Fundamental Solution of a Polyharmonic Equation - Differential Prope@ies of Solutons of a Polyharmonic Equation - Behavior of Polyharmonic Functions in the Neighborhood of Infinity - Almansi's Theorem and Kelvin Transformation - P@ncipal Solutions of a Polyharmonic Equation - Expansion of Polyharmonic Functions in Principal Solutions - Polyharmonic Functons from W,@ in the Neighborhood of Intini@ - Boundary Value Problems for a Polyharmonic Equation in a Bounded Domain - Kelvin of bodies adrature s revised of these s topics Problem in An Infinite Domain - Exterior Variational Problem for a Polyharmonic Equation - Extension of a Funct ion from the Region i2 on R' with the Least Norm - Values of Functions from Wpm) at the Lattice Points Explicit Method of Regularization of Divergent Integrals - TWO SIMPLE PROBLEMS OF THE THEORY OF COMPUTATIONS - Interpolation Construction oi Cubature Formulas - Functional Formulation of the Problems, Extremal Function of a Cubature Formula - Error Functional in W'2 n, (RI Square of the Norm of the Error Functional - Deviation of Error of a Cubature Formula from the Optimal - ORDER OF CONVERGENCE OF CUBATURE FORMULAS - Lower Estimate of the Norm of the Error Functional Approximate Upper Estimate of the Norm of the Error Functional CUBATURE FORMULAS CONSIDERING A REGULAR BOUNDARY LAYER Formulas for Periodic Functions - Norm of the Error Functional for Periodic Functions - Composition of Formulas with Small Suppoas - Error for Finite Functions - Construction of Formulas with a Regular Boundary Layer - Norm of the Error Functional of Cubature Formulas with a Regular Boundary Layer in the Space L(')(R) - Norm of the Error of Formulas with Regular Boundary 2 Layer in L(al(Q) - OPTIMAL FORMULAS - Formulation of the Problem on 2 Optimal Coefficients - Fourier Transformation of a Discrete Potential - Prope@ies of the Operator D(m@[pl' - Discrete Analog of a Polyharmonic h Operator - Optimal Coefficients of One-Dimensional Formulas - CONVERGENCE OF CUBATURE FORMULAS IN VARIOUS CLASSES AND DIFFERENT FUNCTIONS - Functional Class (D(PIA) - Functional Class T(plo) - Cubature Formulas for Infinitely Differentiable Functions - Convergence oi Cubature Formulas for an Arbitrary Function (P(x) c @ll - CUBATURE FORMULAS FOR RATIONAL POLYHEDRA - Convex Polyhedra Euler's Formula - Rational Polyhedra - Structure of Formulas for Rational Polyhedra - Cubature Formulas for a Polyhedron and Its Solid Angles - Formulas with a Formal Boundary Layer
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call