Finite tchebycheff transformations of generalized functions

Abstract

By using Hilbert space techniques, the finite Tchebycheff transformations of the first and the second kind are defined on appropriate spaces of generalized functions. The inversion theorems are established and some operation transform formulas are obtained. These results are applied in solving certain distributional differential equations.

Keywords:

• Generalized functions
• Tchebycheff transformations
• translation
• convolution

AMS:

• 46F12
• 44C20