Complex Analysis and Operator Theory最新文献

We extend constructions of classical Clifford analysis to the case of indefinite non-degenerate quadratic forms. Clifford analogues of complex holomorphic functions—called monogenic functions—are defined by means of the Dirac operators that factor a certain wave operator. One of the fundamental features of quaternionic analysis is the invariance of quaternionic analogues of holomorphic function under conformal (or Möbius) transformations. A similar invariance property is known to hold in the context of Clifford algebras associated to positive definite quadratic forms. We generalize these results to the case of Clifford algebras associated to all non-degenerate quadratic forms. This result puts the indefinite signature case on the same footing as the classical positive definite case.

This paper employs Nevanlinna value distribution theory in several complex variables to explore the characteristics and form of finite as well as infinite order solutions of Circular-type nonlinear partial differential-difference equations in (mathbb {C}^n). The results obtained in this paper contribute to the improvement and generalization of some recent results. In addition, illustrative examples are provided to validate the conclusions drawn from the main results. Moreover, we investigate the infinite-order solutions of Circular-type functional equations in ( mathbb {C}^n ).

In this note, some inequalities involving matrix means of sectorial matrices are proved which are generalizations and refinements of previous known results. Among them, let A and B be two accretive matrices with (A,Bin mathcal {S}_{theta }), (0 < mI leqslant A, B leqslant MI) for positive real numbers M and m. If (sigma ,sigma _1,sigma _2) are matrix means such that (sigma ^*leqslant sigma _1,sigma _2leqslant sigma ), where (sigma ^*) is the adjoint of (sigma ) and (Phi ) is a positive unital linear map, then for each (p>0),

where

and ( K= frac{(M+m)^2}{4mM}) is the Kantorovich constant.

Let (w(zeta )) be a function analytic on ({{mathbb {D}}}), (|w(zeta )|le 1). Let (|t_0|=1). Assume that w and (w') have nontangential boundary values (w_0) and (w'_0), respectively, at (t_0), (|w_0|=1). Then (Carathéodory–Julia) (t_0dfrac{w'_0}{w_0}ge 0). The goal of this paper is to obtain a lower bound on this ratio if w is character-automorphic with respect to a Fuchsian group (Theorem 6.1).

Given a point w in the upper half-plane (Pi _{mathord {+}}), we describe the set of all possible values F(w) of transforms (F(z),{:=},int _{[alpha ,beta ]}(x-z)^{-1}sigma (textrm{d}x)), (zin Pi _{mathord {+}}), corresponding to solutions (sigma ) to a (non-degenerate) truncated matricial Hausdorff moment problem. This set turns out to be the intersection of two matrix balls the parameters of which are explicitly constructed from the given data.

A sequence of operators (T_n) from a Hilbert space ({{mathfrak {H}}}) to Hilbert spaces ({{mathfrak {K}}}_n) which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from ({{mathfrak {H}}}) to a Hilbert space ({{mathfrak {K}}}). Moreover, the closability or closedness of (T_n) is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.

The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.

In this paper, the main aim is to prove the weak type (L log L) estimates for commutators of fractional integral operators and the higher order in the context of the p-adic version of Lebesgue spaces, where the symbols of the commutators belong to the p-adic version of ({text {BMO}}) space. In addition, we also establish the estimates of the sharp function on the p-adic vector space.

In this article we obtain an explicit formula for the Hilbert transform of (log |f|,) for the function f in Nevanlinna class having continuous extension to the real line. This family is the largest possible for which such a formula for the Hilbert transform of (log |f|,) can be obtained. The formula is very general and implies several previously known results.

In our research work, we introduce a new class of operators that we call b-AM-Dunford–Pettis operators. Properties of b-AM-Dunford–Pettis operators, the relationship between the b-AM-Dunford–Pettis operators and various classes of operators are investigated. On the other side, our techniques and results will be related to the lattice structure of the b-AM-Dunford–Pettis operators. For instance, it will be proved that under certain conditions, the b-AM-Dunford–Pettis opertors verify the domination properties.