Integral transforms, reproducing kernels and their appications by S Saitoh instant download

Integral transforms, reproducing kernels and their appications by S Saitoh instant download

This Research Note is an essentially 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 when 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, representations of inverse functions, natural norm inequalities in nonlinear transforms, and stability of Lipschitz type in the determination of initial heat distributions. The general theories and results of the application are fairly elementary, but definite results have been obtained. Mathematicians and scientists will recognize the novelty of the approach.