Lasser R. Introduction to Fourier Series 1996

Textbook in PDF format

Preface
Fourier Coefficients
Approximate Identities
Approximate Identities and Pointwise Convergence
Square Integrable Functions
Convergence of Fourier Series in Norm
Local Convergence
Characterization of Fourier Coefficients
Hilbert Transform
Characterizations of Approximate Identities
Triangular Schemes
Elements of Best Approximation
Poisson Integrals and Hardy Spaces
Conjugation of Approximate Identities
Szegö-Kolmogorov Theorem
Absolute Convergence of Fourier Series
Fourier Transform on R
Plancherel Transform on R
Poisson Summation Formula
Appendices
Appendix A: Measure Theory
Appendix B: Banach Spaces
Appendix C: Banach Algebras
References
Index