We consider functions f of two real variables, given as trigonometric functions over a finite set F of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle 2kπ M for some integer M . Firstly, we address the problem of evaluating these functions over a similar finite set E in the space plane and, secondly, we address the problems of interpolating or appro...

We introduce the notion of a g-atomic subspace for bounded linear operator and construct several useful resolutions identity on Hilbert space using theory g-fusion frames. Also we shall describe concept frame pair Bessel sequences some their properties.

For the general Euler–Poisson–Darboux equation, we prove a theorem on uniqueness of solution Cauchy problem by energy method. The this turns out to be unique only for nonnegative values parameter $$k $$ in Bessel operator acting with respect time variable.

A spectral parameter power series (SPPS) representation for regular solutions of singular Bessel type Sturm-Liouville equations with complex coefficients is obtained as well as an SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. It is proved that the set of zeros of the characteristic function coincides with the set of all ...

In the present paper we consider the heat equation ut = Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients αk(n,m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schrödinger operator. We derive an explicit formula for αk in ter...

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process — a probability measure on a space of countable point configurations. The kernel is expressed in terms of the Whittaker confluent hypergeometric functions. It depends on two parameters and determines a J-symmetric operator K in L(R+)⊕ L(R+). It turns ou...

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous ma...

in this paper we study the duality of bessel and g-bessel sequences in hilbertspaces. we show that a bessel sequence is an inner summand of a frame and the sum of anybessel sequence with bessel bound less than one with a parseval frame is a frame. next wedevelop this results to the g-frame situation.

We use discrete analogs of Riemann–Hilbert problem’s methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define discrete analogs of a Riemann–Hilbert problem and of an integrable integral operator and show that computing the resolvent of a discrete integrable operator can be reduced to solving a corresponding discr...