Related papers: Some Topics Related to Bergman Kernel

Support vector machines and kernel methods are increasingly popular in genomics and computational biology, due to their good performance in real-world applications and strong modularity that makes them suitable to a wide range of problems,…

This is a survey article on Mercer's Theorem in its most general form and its relations with the theory of reproducing kernel Hilbert spaces and the spectral theory of compact operators. We provide a modern introduction to the basics of the…

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is…

As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra. We consider the pull-back of this operation to the moduli space of curves via the Torelli…

We introduce a wider class of bounded Hartogs domains, which contains some generalizations of the classical Hartogs triangle. A sharp criteria for the $L^p-L^q$ boundedness of the Toeplitz operator with symbol $K^{-t}$ is obtained on these…

In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the companion paper to prove an orbifold version of…

In this paper we investigate a class of domains $\Omega^{n+1}_k =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the…

We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.

For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. For Bernstein-Markov measures, this results in the…

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit…

Very recently one has started to study Bergman and Szeg\"o kernels in the setting of octonionic monogenic functions. In particular, explicit formulas for the Bergman kernel for the octonionic unit ball and for the octonionic right…

We organize and review some material from various sources about prepotentials, Riemann surfaces and kernels, WDVV, and the renormalization group, provide some further connections and information, and indicate some directions and problems.

For $1<p<\infty$, we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^p$-Bergman space. The construction gives an integral kernel generalizing the ($L^2$) Bergman kernel. The operator defined by the…

We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel.…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

We investigate domain-wall/quantum field theory correspondences in various dimensions. We give particular emphasis to the special case of the quantum mechanics of 0--branes.

We construct inner products by the Bernstein-Markov inequality on spaces of holomorphic sections of high powers of a line bundle. The corresponding weighted Bergman kernel functions converge to an extremal function. We obtain a uniform…

By introducing a suitable new definition for the inner product on the octonionic Bergman space, we determine the explicit form of the octonionic Bergman kernel, in the framework of octonionic analysis which is non-commutative and…

This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels. Existence and uniqueness properties are carefully reviewed. The approach we follow in this survey uses a more abstract but very…

We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.