Integral Transforms, Reproducing Kernels and Their Applications (Hardcover)

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.