This paper presents a new family of localized orthonormal bases – sinlets – which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic oscillator equation. By construction, each sinlet is infinitely differentiable and has a well-defined and smooth instantaneous frequency known in analytical fo...

Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an element of this superalgebra which turns out to be a dynamical superalgebra for this system. The supercoherent states, defined by means of a supergroup displacemen...

An explicit formula for the chaotic representation of the powers of increments, (Xt+t0 −Xt0) n , of a Lévy process is presented. There are two different chaos expansions of a square integrable functional of a Lévy process: one with respect to the compensated Poisson random measure and the other with respect to the orthogonal compensated powers of the jumps of the Lévy process. Computationally e...

This paper introduces four classes of rotation-invariant orthogonal moments by generalizing four existing moments that use harmonic functions in their radial kernels. Members of these classes share beneficial properties for image representation and pattern recognition like orthogonality and rotation-invariance. The kernel sets of these generic harmonic function-based moments are complete in the...

Adapting ideas of Daubechies and Klauder [J. Math. Phys. 26, 2239 (1985)] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrödinger semigroup on the Hilbert space L2(R2) of Lebesgue square-int...

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we discuss when the irreducibility requirement can be dropped, using a connection between generalized wavelet transforms and Plancherel theory. For unimodular groups ...

We study regression models for the situation where both dependent and independent variables are square integrable stochastic processes. Questions concerning definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical component...

We prove a strong induction theorem and classify the tempered and square integrable representations of graded Hecke algebras.

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker func...