Theory of reproducing kernels and its applications. (English) Zbl 0652.30003

Pitman Research Notes in Mathematics Series, 189. Harlow (UK): Longman Scientific & Technical; New York etc.: John Wiley & Sons. 157 p. £14.50 (1988).
In these lecture notes, Saitoh gives an account of the theory of reproducing kernels and its applications to problems in analysis. These applications include a new characterization of the adjoint of Szegö type kernels, various quadratic norm inequalities, and interpolation problems of Pick-Nevanlinna type. These notes cover other topics as integral transforms, and non harmonic integral transforms.
Reviewer: J.Burbea


30C40 Kernel functions in one complex variable and applications