Orthogonal series. (Ортогональные ряды.) (Russian) Zbl 0632.42017

Kashin, B. S.; Saakyan, A. A.

Moskva: Nauka. 496 p. R. 4.10 (1984).

Annotation: Fundamental methods in the theory of orthogonal series are presented. Orthonormal systems of general type and important concrete systems are studied (for example, the Haar and Franklin systems). Classical results as well as the achievements of the last years are deduced. All propositions, which fall outside the framework of a university course, are presented with full proofs. The book is written for specialists in mathematical analysis and for post graduate students of the corresponding subjects.

MSC:

42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
42-02	Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A20	Convergence and absolute convergence of Fourier and trigonometric series

Keywords:

Haar system; Fourier series; Franklin systems