We show that the average characteristic polynomial P n (z) = E[det(zI−M)] of the random Hermitian matrix ensemble Z −1 n exp(−Tr(V (M) − AM))dM is characterized by multiple orthogonality conditions that depend on the eigenvalues of the external source A. For each eigenvalue a j of A, there is a weight and P n has n j orthogonality conditions with respect to this weight, if n j is the multiplici...

Notions of orthogonality and convolution are explored with the use Kontorovich–Lebedev transform its convolution. New classes corresponding orthogonal polynomials functions investigated. Integral representations, relations explicit expressions established.

j=1 ‖fj‖ 1 n Lavg(BR) p = 2n n− 1 where f = ∑n j=1 fj , supp f̂j ⊂ N1/RΣj and Σj are hypersurfaces with normal vector almost parallel to xj-axis. Take p-th power on both sides and induction on scales. Tile BR using balls of radius R1/2. The averaged integral over BR on the left hand side is approximately the average over all balls of radius R1/2 in the tiling of the averaged integral over one ba...

in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Grünbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.

Orthogonality of polynomials in several variableswith respect to a positiveBorelmeasure supported on an algebraic set is themain theme of this paper.As a step towards this goal quasi-orthogonality with respect to a non-zero Hermitian linear functional is studied in detail; this occupies a substantial part of the paper. Therefore necessary and sufficient conditions for quasi-orthogonality in ter...

Abstract The orthogonality time is examined for different initial states settings interacting locally with types of spin interaction: XX , Ising and anisotropic models. It shown that the number increases, consequently decreases as environment qubits increase. shortest displayed chain model, while largest model. external field increases numbers orthogonality, Dzyaloshinsky–Moriya interaction ort...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...

We study the norm derivatives in context of Birkhoff–James orthogonality real Banach spaces. As an application this, we obtain a complete characterization left-symmetric points and right-symmetric space terms derivatives. strong $$\ell _1^n$$ _\infty ^n$$ also relation defined by some newly introduced variation orthogonality. further orthogonality, approximate smoothness attainment bounded bili...