Complex Analysis and Operator Theory最新文献

In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. In the case of forward and vanishing Bergman Carleson measures, our results extend the results of [J Funct Anal 280(6):26, 2021] from (1leqslant pleqslant q< 2p) to all (0<pleqslant q<infty ). In a more general case, we characterize the positive Borel measures (mu ) on (mathbb {B}) so that the radial differentiation operator (R^{k}:A_omega ^p(mathbb {B})rightarrow L^q(mathbb {B},mu )) is bounded and compact. Although we consider the weighted Bergman spaces induced by two-side doubling weights, the results are new even on classical weighted Bergman spaces.

In this paper, commutativity of the compressions of kth order slant Toeplitz operators is discussed. We show that the commutativity and essential commutativity of two compressions of kth order slant Toeplitz operators on (H^2) are same. We also establish some results on the compactness of the compressions of kth order slant Toeplitz operators. In the last section, we discuss various similarities and differences between compactness and non-compactness of these operators by simply looking at their graphs.

A tuple of commuting Hilbert space operators ((S_1, ldots , S_{n-1}, P)) having the closed symmetrized polydisc

as a spectral set is called a (Gamma _n)-contraction. From the literature we have that a point ((s_1, ldots , s_{n-1},p)) in (Gamma _n) can be represented as (s_i=c_i+pc_{n-i}) for some ((c_1, ldots , c_{n-1}) in Gamma _{n-1}). We construct a minimal (Gamma _n)-isometric dilation for a particular class of c.n.u. (Gamma _n)-contractions ((S_1, ldots , S_{n-1},P)) and obtain a functional model for them. With the help of this model we express each (S_i) as (S_i=C_i+PC_{n-i}), which is an operator theoretic analogue of the scalar result. We also produce an abstract model for a different class of c.n.u. (Gamma _n)-contractions satisfying (S_i^*P=PS_i^*) for each i. By exhibiting a counter example we show that such abstract model may not exist if we drop the hypothesis that (S_i^*P=PS_i^*). We apply this abstract model to achieve a complete unitary invariant for such c.n.u. (Gamma _n)-contractions. Additionally, we present different necessary conditions for dilation and a sufficient condition under which a commuting tuple ((S_1, ldots , S_{n-1},P)) becomes a (Gamma _n)-contraction. The entire program goes parallel to the operator theoretic program developed by Sz.-Nagy and Foias for a c.n.u. contraction.

Cotîrlă and Szász (Comput Methods Funct Theory: 2023) solved a conjecture related with inclusion relation for Bessel functions, proposed by Baricz and András (Complex Var Elliptic Equ 54(7): 689–696, 2009). In this paper, we prove this conjecture for normalized Struve functions by using subordination factor sequences.

In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.

We carry out complete membership to Kaplan classes of functions given by formula

where (nin mathbb N), (t_kin [0;2pi )) and (p_kin mathbb R) for (kin mathbb Ncap [1;n]). In this way we extend Sheil-Small’s, Jahangiri’s and our previous results. Moreover, physical and geometric applications of the obtained gap condition are given. The first one is an interpretation in terms of mass and density. The second one is a visualization in terms of angular inequalities between vectors in (mathbb {R}^2).

This paper presents some inner product inequalities for Hilbert space operators having closed ranges. The obtained results are applied to obtain new bounds for the numerical radius and the operator norm, where the Moore-Penrose inverse plays a keen role.

In this paper, by using the hypergeometric functions, we obtain the formula for the Rawnsley’s (varepsilon )-function of the Kähler manifold ((H^n_{{k_i},gamma },g_{mu ,nu })) with (mu in ({mathbb {R}}^+)^l) and (nu in ({mathbb {R}}^+)^{n-k}), where (H^n_{{k_i},gamma }) is a class of bounded Hartogs domains defined by

and (g_{mu ,nu }) is a Kähler metric associated with the Kähler potential (-sum _{i=1}^lmu _iln (|z_{k+1}|^{2gamma }-Vert {widetilde{z}}_iVert ^2)-sum _{j=k+1}^nnu _jln (|z_{j+1}|^2-|z_j|^2)). As applications of the main result, we obtain the existence of balanced metrics on (H^n_{{k_i},gamma }) and prove that (H^n_{{k_i},gamma }) admits a Berezin quantization.

In the algebra of complex quaternions (mathbb {H(C)}) we consider the left– and right–(psi )–hyperholomorphic functions, and left–(Lambda -psi )–hyperholomorphic functions. We justify the transition in left– and right–(psi )–hyperholomorphic functions to a simpler basis i.e., to the Cartan basis. Using Cartan’s basis we find the solution of Cauchy–Fueter equation. By the same method we find representations of left– and right–(psi )–hyperholomorphic functions, and representation of left–(Lambda -psi )–hyperholomorphic functions.

This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces (mathcal {F}(Omega )) of continuous functions on a Hausdorff space (Omega ) such that the norm-topology is stronger than the compact-open topology like the Hardy spaces, the weighted Bergman spaces, the Dirichlet space, the Bloch type spaces, the space of bounded Dirichlet series and weighted spaces of continuous or holomorphic functions. It was shown by Gallardo-Gutiérrez, Siskakis and Yakubovich that there are no non-trivial norm-strongly continuous weighted composition semigroups on Banach spaces (mathcal {F}(mathbb {D})) of holomorphic functions on the open unit disc (mathbb {D}) such that (H^{infty }subset mathcal {F}(mathbb {D})subset mathcal {B}_{1}) where (H^{infty }) is the Hardy space of bounded holomorphic functions on (mathbb {D}) and (mathcal {B}_{1}) the Bloch space. However, we show that there are non-trivial weighted composition semigroups on such spaces which are strongly continuous w.r.t. the mixed topology between the norm-topology and the compact-open topology. We study such weighted composition semigroups in the general setting of Banach spaces of continuous functions and derive necessary and sufficient conditions on the spaces involved, the semiflows and semicocycles for strong continuity w.r.t. the mixed topology and as a byproduct for norm-strong continuity as well. Moreover, we give several characterisations of their generator and their space of norm-strong continuity.