In this paper, we shall study differential geometric properties of bounded domains in Cn. Here is the summary of our results. We consider an w-dimensional complex manifold M and the Hilbert space of square integrable holomorphic re-forms on M. After Bergman [3; 4; 5], we define the kernel form on M (instead of the kernel function) and, under certain assumptions, we define the invariant metric o...

The refined x-ray crystal structure of the phase Mg(27)Al(10.7(2))Zn(47.3(2)) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsu...

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

For distributed arithmetic the latency is proportional to the maximal number of fractional bits for any coefficient. When implementing recursive filters this is a disadvantage as the resulting minimal sample period may be longer compared with an implementation using separate multiplications and additions. In this paper we propose a method to decrease the latency for inputs where the correspondi...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...

The (k, r) admissible Jack polynomials, recently proposed as many-body wavefunctions for non-Abelian fractional quantum Hall systems, have been conjectured to be related to some correlation functions of the minimal model WAk−1(k+1, k+r) of the WAk−1 algebra. By studying the degenerate representations of this conformal field theory , we provide a proof for this conjecture. PACS numbers: 75.50.Lk...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

The fractional level models are (logarithmic) conformal field theories associated with affine Kac-Moody (super)algebras at certain levels k ∈Q. They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved. Here, Wakimoto’s free field realisation is combined with the theory of Jack symmetric functions to analyse the fractional level ŝl(2) mo...