Preface to the Second Edition
Preface to the First Edition
Contents
1 Hilbert Spaces
1.1 Complete Sets, Fourier Expansions
1.1.1 Preliminary Notions. Subspaces. Complete Sets
1.1.2 Fourier Expansions
1.1.3 Harmonic Functions; Dirichlet and Neumann Problems
1.2 Linear Operators in Hilbert Spaces
1.2.1 A Survey of General Properties of Operators
1.2.2 Linear Operators Defined Giving Ten=vn, and Related Problems
1.2.3 Operators of the Form Tx=v(w,x) and Tx=sumn vn(wn,x)
1.2.4 Operators of the Form Tf(x)=Ο(x)f(x)
1.2.5 Problems Involving Differential Operators
1.2.6 Functionals
1.2.7 Time-Evolution Problems. Heat Equation
1.2.8 Miscellaneous Problems
2 Functions of a Complex Variable
2.1 Basic Properties of Analytic Functions
2.2 Evaluation of Integrals by Complex Variable Methods
2.3 Harmonic Functions and Conformal Mappings
3 Fourier and Laplace Transforms. Distributions
3.1 Fourier Transform in L1(R) and L2(R)
3.1.1 Basic Properties and Applications
3.1.2 Fourier Transform and Linear Operators in L2(R)
3.2 Tempered Distributions and Fourier Transforms
3.2.1 General Properties
3.2.2 Fourier Transform, Distributions and Linear Operators
3.2.3 Applications to ODE's and Related Green Functions
3.2.4 Applications to General Linear Systems and Green Functions
3.2.5 Applications to PDE's
3.3 Laplace Transforms
4 Groups, Lie Algebras, Symmetries in Physics
4.1 Basic Properties of Groups and of Group Representations
4.2 Lie Groups and Lie Algebras
4.3 The Groups SO3,SU2,SU3
4.4 Other Relevant Applications of Symmetries to Physics
Answers and Solutions
Problems of Chap.
1
Problems of Chap. 2
Problems of Chap. 3
Problems of Chap. 4
Bibliography