This volume is essentially a self-contained presentation of the theory of reproducing kernels in connection with integral transforms in the framework of Hilbert spaces. It is a general and fundamental concept and a potentially powerful theory combined with the integral transforms. A variety of concrete results of its application are given systematically for isometrical identities and inversion formulas for various typical integral transforms, best approximation theories of functions, analytic extension formulas, real inversion formulas for the Laplace transform, inverse source problems,...

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.
Audience: Researchers and graduate students in complex analysis, partial differential equations,...

The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we...

Analytic Extension is a mysteriously beautiful property of analytic functions. With this point of view in mind the related survey papers were gathered from various fields in analysis such as integral transforms, reproducing kernels, operator inequalities, Cauchy transform, partial differential equations, inverse problems, Riemann surfaces, Euler-Maclaurin summation formulas, several complex variables, scattering theory, sampling theory, and analytic number theory, to name a few.
Audience: Researchers and graduate students in complex analysis, partial differential equations,...