Covariant Transform

Abstract

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. Covariant transform extends an applicability of the popular wavelets construction to classic examples like the Hardy space H_2, Banach spaces, covariant functional calculus and many others. Keywords: Wavelets, coherent states, group representations, Hardy space, Littlewood-Paley operator, functional calculus, Berezin calculus, Radon transform, Moebius map, maximal function, affine group, special linear group, numerical range, characteristic function, functional model.

9 pages, LaTeX2e (AMS-LaTeX); v2: minor corrections

References in corpus (2)

• Coherent States for the Hydrogen Atom
• Analysis in $R^{1,1}$ or the Principal Function Theory

Cited by in corpus (5)

• Erlangen Programme at Large: An Overview
• Wavelets from Laguerre polynomials and Toeplitz-type operators
• Geometric Dynamics of a Harmonic Oscillator, Arbitrary Minimal Uncertainty States and the Smallest Step 3 Nilpotent Lie Group
• Cross-Toeplitz Operators on the Fock--Segal--Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
• Metamorphism as a covariant transform for the SSR group