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Abstract
A general method for integral transforms in the framework of Hilbert spaces is introduced, and its miscellaneous applications are given.
Keywords:
- Hilbert space
- reproducing kernel
- linear transform
- integral transform
- inversion formula
- Pythagoras' theorem
- Fredholm integral equation of the first kind
- heat equation
- wave equation
- analytic extension
- ill and well-posed problems
- sampling theorem
- best approximation
- random estimation
- scattering problem
- inverse problem
- norm inequality
- nonharmonic transform
- wavelets