Related papers: A Tale of Three Kernels
We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion)…
In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…
We study the Kohn-Laplacian and its fundamental solution on some model domains in $\mathbb C^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szeg\"o projections on these model domains using the real analysis method. We further…
The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also introduce two additional reproducing kernel Hilbert spaces…
We consider a bounded domain $\Omega \subseteq \mathbb C^d$ which is a $G$-space for a finite complex reflection group $G$. For each one-dimensional representation of the group $G,$ the relative invariant subspace of the weighted Bergman…
The notions of the kernel of a graph, full truth sets and full satisfaction sets are connected.
We discuss some recent developments in the description of baryons as three-quark systems within relativistic constituent quark models. In particular we address the issues of excitation spectra, electroweak structure, and mesonic resonance…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
Multi-party object coordination - across object-capability systems, smart-contract platforms, distributed actors, and event-sourced architectures - is shaped by six structural properties: authenticated provenance, opaque encapsulation,…
We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erd\"os and H. Fried) of the so called Szeg\"o's power series. This characterization is then applied to readily…
The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.
There are suggestive experimental indications that the leptons, neutrinos, and quarks are composite and that their structure is described by the quantum group SLq(2). Since the hypothetical preons must be very heavy relative to the masses…
The ``preon-trinity'' model for the compositeness of leptons, quarks and heavy vector bosons predicts several new heavy leptons and quarks. Three of them can be produced in $e^{+}e^{-}$ annihilations at CERN LEP energies, since they can be…
The cyclic product of an arbitrary number of Szeg\"o kernels for even spin structure $\delta$ on a compact higher-genus Riemann surface $\Sigma$ may be decomposed via a descent procedure which systematically separates the dependence on the…
We compute the Szeg\"o kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not…
A model is presented of the leptons, quarks and bosons as non-elementary particles being composed of spinons. They are defined as massless fermions obeying the Weyl equations, but in addition are charged and assumed to have two internal…
If this article, an elementary kernel-cokernel exact sequence is introduced for $A\stackrel{f}\to B\stackrel{g}\to C$. Some relative sequences and applications are dicussed. This result can simplify some proofs---the indices of Frodholm…
We give a brief account of a construction called tokens here, which is significant in algebra, analysis, combinatorics, and physics. Tokens allow to express a semigroup on one set via a semigroup convolution on another set. Therefore tokens…
This talk briefly discusses the set of meson resonances discovered in the latest decade. They are frequently treated in the literature as tetraquarks or hadron molecules. Our consideration (using the energy-time uncertainty relation)…