Accelerating infinite products

Slowly convergent infinite products are considered, where is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the “remainder” of the infinite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences . For complicated sequences it involves the solution of some linear systems, but it is still effective. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the dimension of almost -dimensional spaces

Oversteegen and Tymchatyn proved that homeomorphism groups of positive dimensional Menger compacta are -dimensional by proving that almost -dimensional spaces are at most -dimensional. These homeomorphism groups are almost -dimensional and at least -dimensional by classical results of Brechner and Bestvina. In this note we prove that almost -dimensional spaces for are -dimensional. As a corollary we answer in the affirmative an old question of R. Duda by proving that every hereditarily locally connected, non-degenerate, separable, metric space is -dimensional.

     

Extension theory approach to scattering and annihilation in the\bar pd system

We consider the problems of three-particle scattering and annihilation in a system of three strongly interacting charged particles ( pn). We propose a model for the elastic scattering and the breakup process in the nucleon channel as well as for the annihilation into mesons. The mathematical foundation of the model is the extension theory of symmetrical operators. In the framework of this model, we construct the modified integral Faddeev equations with energy-dependent interactions taking the annihilation processes into account. These equations are uniquely resolvable for suitable classes of functions. On this basis, we deduce the corresponding differential Faddeev equations, construct asymptotic boundary conditions for wave function components, and formulate boundary problems for a system composed of nucleonic and mesonic channels. The results obtained are applied to scattering and annihilation processes in the three-particle system . Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 74–94, January, 1999.     

On one property of the Dirac equations for a free particle of spin ħ/2

We pose and investigate the general problem of the transformation of the Dirac equation for a free spin /2 particle to a form in which the Schrodinger Zitterbewegung (SZ) is absent. Equations are obtained which define a unitary transformation which eliminates SZ in the Dirac theory. Analysis of these equations shows that only partial removal of SZ along one of the coordinate axes is possible. Complete elimination of SZ in the Dirac theory is impossible. In conclusion we examine the possible existence of a whole class of unitary transformations which partially remove SZ and their connection with the known canonical transformations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 33–36, 1972.In conclusion the author would like to thank S. V. Izmailov, I. L. Gerlovin, and E. M. Levin for useful discussions of the questions investigated in the paper.     

The numerical radius and specttural matrices

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.