Pseudodifferential operators on ultrametric spaces and ultrametric wavelets

Details Pseudodifferential operators on ultrametric spaces and ultrametric wavelets Pseudodifferential operators on ultrametric spaces and ultrametric wavelets

2004-12-17

arxiv.org/abs/math-ph/0412062v1

Izv.Math.69:989-1003,2005

Physics

Mathematical Physics

19 pages, LaTeX

Scientific paper

A family of orthonormal bases, the ultrametric wavelet bases, is introduced in quadratically integrable complex valued functions spaces for a wide family of ultrametric spaces. A general family of pseudodifferential operators, acting on complex valued functions on these ultrametric spaces is introduced. We show that these operators are diagonal in the introduced ultrametric wavelet bases, and compute the corresponding eigenvalues. We introduce the ultrametric change of variable, which maps the ultrametric spaces under consideration onto positive half-line, and use this map to construct non-homogeneous generalizations of wavelet bases.

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