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.

Anum ber of spectral modeling approaches in the engineering and estimation lit.erature are potentially applicable to stochas. ic synthesis in computer graphics. Two specific approaches are developed. The orthogonality principle of estimation theory is used to derive a stochastic subdivision construction with specified autocorrelation and spectrum properties; this approach also provides an alter...

The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey– Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynom...

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 spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...

In this paper, we propose a parametric solution to the partial eigenvalue assignment problem by state feedback control for non-symmetric quadratic pencil in multi-input case using orthogonality relations between eigenvectors. Our solution can be implemented with only a partial knowledge of the spectrum and the corresponding eigenvectors of non-symmetric quadratic pencil. We show that the number...

We investigate the system of a heavy impurity embedded in paired two-component Fermi gas at crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid via an extension functional determinant approach (FDA). FDA is exact numerical applied study manifestations Anderson's orthogonality catastrophe (OC) static immersed ideal gas. Here, we extend strongly correlated ...

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.

Multicarrier spread spectrum (MC-SS) systems exhibit good robustness against all kinds of narrowband interference, coloured noise or selective attenuation for power line communications. However, the systems’ vulnerability to frequency synchronization errors, which introduce loss of orthogonality between the subcarriers, is still a challenging problem for robust communications. This paper presen...