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...

Whittaker 's sampling theorem (Whittaker, 1915; McNamee et al., 1971) for the reconstruction of a frequency-band-limited time-function g(t), f rom its uniform (i.e., equidistant) samples g(k); k ~ J (the class of integers); has been extended by Fogel (1955) and Jagerman and Fogel (1956) to include the simultaneous sampling of g(t) and its first derivative. Fogel's work (1955) is quite incomplet...

Résumé Soit G un groupe réductif p-adique et U0 le radical unipotent d’un sousgroupe parabolique minimal de G. Nous introduisons une transformation de Fourier pour l’espace des fonctions de Whittaker lisses sur G et à support compact modulo U0. Nous en déterminons l’image. La preuve suit celle d’Heiermann pour les fonctions sur le groupe. Au cours de la preuve, une formule d’inversion est prouv...

vegetation studies measuring the accuracy of the results is important. the purpose of this study is to compare shape and distribution plots on different levels for species richness measurements.thiscomparison was in three design whittaker, stohlgern and a new design (ariz) in ariz, sanandaj.designed proposition (ariz) obtainedon base changes in the size and distribution plotin design stohlgern ...

1.1 One of the important technical tools in D. Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GLn. In this paper we define analogous functors for GSp4 and study their properties. Let us first review the situation at the level of automorphic forms on G = Sp4. Let X be a smooth projective absolutely i...

Socio-Technical Lifelogging: Deriving Design Principles for a Future Proof Digital Past Steve Whittaker a , Vaiva Kalnikaitė b , Daniela Petrelli c , Abigail Sellen d , Nicolas Villar d , Ofer Bergman e , Paul Clough f & Jens Brockmeier g h a University of California at Santa Cruz b Interactables, Cambridge, United Kingdom c Sheffield Hallam University, United Kingdom d Microsoft Research Cambr...

Abstract. This article considers Whittaker’s confluent hypergeometric function Wκ,μ where κ is real and μ is real or purely imaginary. Then φ(x) = xWκ,μ(x) arises as the scattering function of a continuous time linear system with state space L(1/2,∞) and input and output spaces C. The Hankel operator Γφ on L(0,∞) is expressed as a matrix with respect to the Laguerre basis and gives the Hankel m...