Complex Analysis and Operator Theory最新文献

In this work, we consider the spectral problems for the Sturm–Liouville operators on a caterpillar graph with the standard matching conditions in the internal vertices and the Neumann or the Dirichlet conditions in the boundary vertices. The regularized trace formulae of these operators are established by using the residue techniques of complex analysis.

We describe ten geometric functionals, four real and six complex, which determine the geometry of five point sets in the complex ball up to conformal automorphism. We give conditions on those parameters which are necessary and sufficient for there to be an associated five point set.

The estimation of zeros of a polynomial with quaternionic coefficients has been done by many mathematicians in the recent past using various approaches. In this paper, we estimate the upper bounds for the zeros of polynomials and derive zero-free regions of some special regular functions of a quaternionic variable with restricted coefficients using the extended Schwarz’s lemma and the zero sets of a regular product. The obtained results for this subclass of polynomials and regular functions produce generalizations of a number of results known in the literature on this subject.

We call the solution of a kind of second order homogeneous partial differential equation as real kernel (alpha )-harmonic mappings. In this paper, the representation theorem, the Lipschitz continuity, the univalency and the related problems of the real kernel (alpha )-harmonic mappings are explored.

This paper is devoted to the study of the S-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S-spectrum. Furthermore, we introduce the left and right Browder S-resolvent operators. Inspired by the S-resolvent equation, we give the Browder’s S-resolvent equation in quaternionic setting.

The composition operator (C_{phi _a}f=fcirc phi _a) on the Hardy–Hilbert space (H^2({mathbb {D}})) with affine symbol (phi _a(z)=az+1-a) and (0<a<1) has the property that the Invariant Subspace Problem for complex separable Hilbert spaces holds if and only if every minimal invariant subspace for (C_{phi _a}) is one-dimensional. These minimal invariant subspaces are always singly-generated ( K_f:= overline{textrm{span} {f, C_{phi _a}f, C^2_{phi _a}f, ldots }}) for some (fin H^2({mathbb {D}})). In this article we characterize the minimal (K_f) when f has a nonzero limit at the point 1 or if its derivative (f') is bounded near 1. We also consider the role of the zero set of f in determining (K_f). Finally we prove a result linking universality in the sense of Rota with cyclicity.

In this paper, we establish some truncated second main theorems for holomorphic curve from an annulus into ({mathbb {P}}^n({mathbb {C}})) and moving hyperplanes. We also use these results to solve unique problems with moving targets.

In this paper, we establish an analogue of Hardy’s theorems for the linear canonical Dunkl transform and fractional Dunkl transform, which generalizes a large class of a family of integral transforms. As application, we derive Hardy type theorems for fractional Hankel type transform, one dimension Dunkl Fresnel transform, linear canonical transform and fractional Fourier transform.

The complex symmetric linear combinations of composition operators on the McCarthy–Bergman spaces of Dirichlet series are completely characterized. The normality and self-adjointness of complex symmetric linear combinations of composition operators on such spaces are also characterized. Some images are given in order to find some interesting phenomena of ({mathcal {J}})-symmetric such combinations.

Abstract

We obtain the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem on the interval [a, b] in case of an even and odd number of moments expressed in terms of terminal point b. An explicit relation between the resolvent matrices of the THMM problem with respect to terminal points a and b is presented.