相关论文: Some topics in complex and harmonic analysis, 5

For a class of variational problems with linear differential operator, we obtain a convenient form of the deviation identity, i.e., the value of the distance between approximated solutions and the exact ones. We illustrate the result with…

A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving…

We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.

We establish some properties of \'etoiles and associated valuations over complex analytic spaces, showing that Abhyankar's inequality holds. We give some examples of pathological behavior of these valuations. We prove a regularization…

We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…

We highlight an intrinsic connection between classical quadrature domains and the well-studied theme of removable singularities of analytic sets in several complex variables. Exploiting this connection provides a new framework to recover…

We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work…

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…

Recently, the degenerate harmonic and the degenerate hyperharmonic numbers are introduced respectively as degenerate versions of the harmonic and the hyperharmonic numbers. The aim of this paper is to introduce the degenerate…

The relations and differences between various classification problems arising in the context of local two-dimensional conformal QFT, modular invariants, and subfactors are discussed. The extent to which locality implies modular invariance,…

Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…

These notes, connected to a "potpourri" topics course currently underway, are concerned with some interrelated themes of polynomials, functions on the unit circle or interval, and norms.

In the present work we recall and extend the results of previous work concerning the time evolution of open quantum systems. We show how general properties of such systems are related to their structure properties, those of their…

Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.

Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of "identifiability", a common property of…

Using the recently developed mathematical theory of tangles, we re-assess the mathematical foundations for applications of the five factor model in personality tests by a new, mathematically rigorous, quantitative method. Our findings…

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.

By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…

We consider 5-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we give a partial classification of left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local…