APPLIED MATHEMATICAL METHODS IN THEORETICAL PHYSICS

By L. FAZAD

CONTENTS INTRODUCTION FUNCTION SPACES, LINEAR OPERATORS AND GREEN’S FUNCTIONS FUNCTION SPACES ORTHONORMAL SYSTEM OF FUNCTIONS LINEAR OPERATORS EIGENVALUES AND EIGENFUNCTIONS THE FREDHOLM ALTERNATIVE SELF-ADJOINT OPERATORS GREEN’S FUNCTIONS FOR DIFFERENTIAL EQUATIONS REVIEW OF COMPLEX ANALYSIS REVIEW OF FOURIER TRANSFORM INTEGRAL EQUATIONS AND GREEN’S FUNCTIONS INTRODUCTION TO INTEGRAL EQUATIONS RELATIONSHIP OF INTEGRAL EQUATIONS WITH DIFFERENTIAL EQUATIONS AND GREEN’S FUNCTIONS STURM–LIOUVILLE SYSTEM GREEN’S FUNCTION FOR TIME-DEPENDENT SCATTERING PROBLEM LIPPMANN–SCHWINGER EQUATION PROBLEMS FOR CHAPTER INTEGRAL EQUATIONS OF VOLTERRA TYPE ITERATIVE SOLUTION TO VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND SOLVABLE CASES OF VOLTERRA INTEGRAL EQUATION INTEGRAL EQUATIONS OF THE FREDHOLM TYPE ITERATIVE SOLUTION TO THE FREDHOLM INTEGRAL EQUATION OF THE SECOND KIND RESOLVENT KERNEL PINCHERLE–GOURSAT KERNEL FREDHOLM THEORY FOR A BOUNDED KERNEL SOLVABLE EXAMPLE FREDHOLM INTEGRAL EQUATION WITH A TRANSLATION KERNEL SYSTEM OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND HILBERT–SCHMIDT THEORY OF SYMMETRIC KERNEL REAL AND SYMMETRIC MATRIX REAL AND SYMMETRIC KERNEL BOUNDS ON THE EIGENVALUES RAYLEIGH QUOTIENT COMPLETENESS OF STURM–LIOUVILLE EIGENFUNCTIONS GENERALIZATION OF HILBERT–SCHMIDT THEORY GENERALIZATION OF STURM–LIOUVILLE SYSTEM