Related papers: Bicomplex Bergman spaces on bounded domains

Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in…

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…

We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of…

For an infinite chain bicomplex we show that the orthogonality and grading conditions provide it with the structure of a bigraded differential algebra with respect to a natural multiplication of several elements bicomplex spaces.…

Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…

We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also…

Two Kahler manifolds are called relatives if they admit a common Kahler submanifold with the same induced metrics. In this paper, we show that a Hartogs domain over an irreducible bounded symmetric domain equipped with the Bergman metric is…

With the advent of kernel methods, automating the task of specifying a suitable kernel has become increasingly important. In this context, the Multiple Kernel Learning (MKL) problem of finding a combination of pre-specified base kernels…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

In this paper we continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind.…

Bregman divergences play a pivotal role in statistics, machine learning and computational information geometry. Particularly in the context of machine learning, they are central to clustering, exponential families, parameter estimation and…

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…

We prove the boundedness of Bergman type projections in two different analytic function spaces in bounded strongly pseudoconvex domains with the smooth boundary. Our results were previously well-known in the case of the unit disk.

In this article, we consider Bergman kernels related to modules at boundary points for singular hermitian metrics on holomorphic vector bundles, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a…

We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a positive $U_q\frak{su}_{nm}$-invariant integral (see…