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, representationbs of inverse functions, natural norm
inequalities in nonlinear transforms and stability of Lipschitz
type in determintion of initial heat distribution.
General
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