We prove that every irreducible, admissible representation π of GSp(4, F ), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided π is not onedimensional. If π is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by π, and prove that Bessel functionals of a fixed type are unique. If π is supercuspidal, we do the...

In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that...

A two-parameter sequence of orthogonal polynomials {Pn(x;λ,t)}n≥0 with respect to the weight function xαe−λxρν(xt),α>−1,λ,t≥0,ρν(x)=2xν/2Kν(2x),x>0,ν≥0, where Kν(z) is modified Bessel function, investigated. The case λ=0 corresponds Prudnikov and t = 0 related Laguerre polynomials. special one-parameter {Pn(x;1−t,t)}n≥0,t∈[0,1] analysed as well.

In this dissertation, we study the Feichtinger Conjecture(FC), which has been shown to be equivalent to the celebrated Kadison-Singer Problem. The FC states that every norm-bounded below Bessel sequence in a Hilbert space can be partitioned into finitely many Riesz basic sequences. This study is divided into two parts. In the first part, we explore the FC in the setting of reproducing kernel Hi...

Using an extension of the Cox-Ingersoll-Ross [1] stochastic model of the short interest rate r, we study the convergence in law of the longterm return in order to make some approximations. We use the theory of Bessel processes and observe the convergence in law of the sequence (√ −2β3 δn ∫ nt 0 (Xu + δu 2β )du ) t≥0 with the X a generalized Besselsquare process with drift with stochastic revers...

introduction: follicle stimulating hormone (fsh) is one of the pituitary glycoproteines that it consists of two subunits alpha and beta. the beta subunit is responsible for the biological activity of fsh. the aim of present study was isolation of the β subunit coding sequence containing its signal sequence from human genome and then cloning of the isolated sequence in ppic9 shuttle vector under...

The theory of localized frames is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet frames. Using the new notion of a R-dual sequence associated with a Bessel sequence, we derive several duality principles concerning localization in abstract frame theory. As applications of our results we prove a duality princi...