We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer G-functions or Wright’s generalized Bessel functions. They generalize in a natural wa...

In this paper we investigate Bessel sequences in the space L2(R s), in Sobolev spaces Hμ(Rs) (μ > 0), and in Besov spaces B μ p,p(R s) (1 p ∞). For each j ∈ Z, let Ij be a countable index set. Let (ψj,α)j∈Z, α∈Ij be a family of functions in L2(R). We give some sufficient conditions for the family to be a Bessel sequence in L2(R s) or Hμ(Rs). The results obtained in this paper are useful for the...

We shall see that in these cases the spectra come from irreducible representations of G occurring in L2(Γ\G), and that the resulting integral transform of g has a kernel composed of Bessel functions of representations of G. It should be noted that (2) can readily be extended to any imaginary quadratic number field of class number one. Other examples that share the same structure and have been m...

We obtain several new closed-form expressions for the evaluation of a family of infinite-domain integrals of the Whittaker functions W , x and M , x and the modified Bessel functions I x and K x with respect to the index . The new family of definite integrals is useful in a variety of contexts in mathematical physics. In particular, the integral involving K x represents a new example of the Kon...

The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with a Bessel process we get a continuum of non-isomorphic product systems.

The paper advances Odake and Sasaki’s idea to re-write eigenfunctions of rationally deformed Morse potentials in terms Wronskians Laguerre polynomials the reciprocal argument. It is shown that constructed quasi-rational seed solutions Schrödinger equation with potential are formed by generalized Bessel degree-independent indexes. As a new achievement we can point construction Darboux-Crum net i...

Controlled g-atomic subspace for a bounded linear operator is being presented and characterization has been given. We give an example of controlled K-g-fusion frame. construct new frame the Hilbert space H ? X using frames spaces X. Several useful resolutions identity on theory g-fusion have discussed. Frame pair Bessel sequences introduced.