in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.

Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for...

We complete the one loop renormalization of the HQET lagrangian at O(1/mQ) including four fermion operators with two heavy and two light quark fields in the operator basis. It is shown that as a consequence the short distance coefficients of the operators bilinear in the heavy quark field receive nontrivial corrections. ¶email: [email protected]

A bilinear selection scheme for ranked populations is presented. The deVelopment of the selection scheme is motivated by the desire for a generationally dependant selection mechanism that can be adjusted in an intuitive manner. The selection mechanism is dehned by a four parameter (p, l, c, B) bilinear cumulative probabiliry distribution. Expressions for the mean and variance of the proposed bi...

The inverse problem of the calculus variations (IPCV) is solved for a second-order ordinary differential equation with use local bilinear form. We apply methods analytical dynamics, nonlinear functional analysis, and modern solving IPCV. In paper, we obtain necessary sufficient conditions given operator to be potential relative form, construct corresponding functional, i.e., found solution IPCV...

We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky’s (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra sl 2 .

Four-point correlation functions of hypermultiplet bilinear composites are analysed in N = 2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is shown that the complete amplitude is determined by a single arbitrary function of the two conformal cross-ratios of the space-time variables.

We complete the one loop renormalization of the HQET lagrangian at O(1/m3Q) including four fermion operators with two heavy and two light quark fields in the operator basis. It is shown that as a consequence the short distance coefficients of the operators bilinear in the heavy quark field receive nontrivial corrections. email: [email protected]