Orthogonal harmonic analysis of fractal measures.
Wavelet constructions in non-linear dynamics.
Approximately Invariant Subspaces for Unbounded Linear Operators. II.
Partial Differential Operators and Discrete Subgroups of a Lie Group.
Unitary dilations of commutation relations asscociated to alternating bilinear forms.
Essential Self-Adjointness of Semibounded Operators.
On Optimal Spectral Estimator for Multi-Dimensional Time Series with an Infinite Number of Sample Points.
Selfadjoint Extension Operators Commuting with an Algebra.
Positive Definite Functions on the Heisenberg Group.
Wavelets on fractals.
We show that there are Hilbert spaces constructed from the Hausdorff measures H on the real line R with 0 < s < 1 which admit multiresolution wavelets. For the case of the middle-third Cantor set C ⊂ [0,1], the Hilbert space is a separable subspace of L(R, (dx)) where s = log(2). While we develop the general theory of multiresolutions in fractal Hilbert spaces, the emphasis is on the case of scale 3 which covers the traditional Cantor set C.
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