Hankel convolution operators on entire functions and distributions

In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration.     

The rank of Hankel operators on harmonic Bergman spaces

We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

     

Trace Extensions,Determinant Bundles,and Gauge Group Cocycles

We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.     

Some inequalities for characteristic functions. II

Recently we established Matysiak and Szablowski's conjecture [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] about a lower bound of real-valued characteristic functions. In this paper, applying an alternative approach we are able to give explicitly the ranges of argument for which the obtained inequalities hold true for general characteristic functions.     

On multiple integrals of special form

Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Adjugates in Banach algebras

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

     

Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

与单形外接球心有关的一个不等式

若n维单形A＝A1A2…An r的外接球心O位于其内部，单形A与单形Ai＝A1A2…Ai-1OAi 1…An 1的外接球半径分别为R与Ri(i=1,2,…,n 1），本文证明了：n 1↑П↑i=1Ri≥(nR/2)^n 1，而等号成立的充分必要条件为单形A正则。