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Orthogonally additive holomorphic functions of bounded type over C(K)
(Cambridge University Press, 2010-10)
It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such ...
Spherical Functions: The Spheres Vs. The Projective Spaces
(Heldermann Verlag, 2014-01)
In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...
Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
(Springer, 2017-06)
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised ...
Chapter 7: A further look at time-and-band limiting for matrix orthogonal polynomials
(World Scientific Publishing Co, 2018)
We extend to a situation involving matrix-valued orthogonal polynomials, a scalar result that originates in work of Shannon and a ground-breaking series of papers by Slepian, Landau and Pollak at Bell Labs in the 1960s. ...
Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots
(American Physical Society, 2010-04)
Resonance states of a two-electron quantum dots are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a ...
Matrix elements of irreducible representations of SU(n + 1)×SU(n + 1) and multivariable matrix-valued orthogonal polynomials
(Academic Press Inc Elsevier Science, 2020-04-15)
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking ...
Emergence of power law distributions for odd and even lifetimes
(American Physical Society, 2020-12-24)
Avalanche lifetime distributions have been related to first-return random walk processes. In this sense, the theory for random walks can be employed to understand, for instance, the origin of power law distributions in ...
A Robust Orthogonal Adaptive Approach to SISO Deconvolution
(Hindawi Publishing Corporation, 2004-10)
This article presents a design procedure for an adaptive deconvolution processor with an orthogonal structure provided by a family of basis functions. The processor is designed to be robust to small parametric uncertainties ...
Spherical Functions of Fundamental K-Types Associated with the n-Dimensional Sphere
(Natl Acad Sci Ukraine, 2014-01)
In this paper, we describe the irreducible spherical functions of fundamentalK-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that ...
On the maximal function for the generalized Ornstein-Uhlenbeck semigroup
(Natl Inquiry Services Centre Pty Ltd, 2007-12)
In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials (Hμn) and prove that it is weak type (1,1) with respect to dλμ(x) = ...