Complex Analysis and Operator Theory
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Tolokonnikov’s Lemma for Real H∞ and the Real Disc Algebra
Complex Analysis and Operator Theory - Tập 1 - Trang 439-446 - 2007
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
$${{H^{\infty}_{\mathbb{R}}}}$$
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with respect to fixed orthonormal bases) are functions having re......
Representable Projections and Semi-Projections in a Hilbert Space
Complex Analysis and Operator Theory - Tập 15 - Trang 1-28 - 2021
Let
$$H = {\mathcal H}\oplus {\mathcal K}$$
be the direct sum of two Hilbert spaces. In this paper we characterise the semi-projections (defined in the paper) and projections with a given kernel and a given range that can be described by a two by two matrix or block of relations determined by the ......
Về giả thuyết BMV cho ma trận 2 $$\times $$ 2 và tính lồi theo cấp số mũ của hàm $${\cosh (\sqrt{at^2+b})}$$ Dịch bởi AI
Complex Analysis and Operator Theory - Tập 11 - Trang 843-855 - 2015
Giả thuyết BMV cho rằng đối với các ma trận Hermitian $$n\times n$$ $$A$$ và $$B$$, hàm $$f_{A,B}(t)={{\mathrm{trace\,}}}e^{tA+B}$$ có tính lồi theo cấp số mũ. Gần đây, giả thuyết BMV đã được Herbert Stahl chứng minh. Chứng minh của Herbert Stahl dựa trên những xem xét tinh vi liên quan đến mặt Riemann của các hàm đại số. Trong bài báo này, chúng tôi đưa ra một chứng minh hoàn toàn "ma trận" của g......
Weak Solutions to the Complex m-Hessian Equation on Open Subsets of $${{\mathbb {C}}}^{n}$$
Complex Analysis and Operator Theory - Tập 13 - Trang 4007-4025 - 2019
In this paper, we prove the existence of weak solutions to the complex m-Hessian equations in the class
$${\mathcal {D}}_{m}(\Omega )$$
on an open subset
$$\Omega $$
......
Extension of the Bessmertnyĭ Realization Theorem for Rational Functions of Several Complex Variables
Complex Analysis and Operator Theory - - 2021
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of Bessmertnyĭ (in: Alpay, Gohberg, Vinnikov (eds) Interpolation Theory, Systems Theory and Related Topics. Operator Theory Advances and Applications vol 134. Birkhauser Verlag, Basel, pp 157–185, 2002). In contrast to Bessmertnyĭ’s approach of solving large systems of linear equations......
The Singular Integral Operator Induced by Drury–Arveson Kernel
Complex Analysis and Operator Theory - Tập 12 - Trang 917-929 - 2016
In this paper, we study the singular integral operator induced by the reproducing kernel of the Drury–Arveson space
$$\begin{aligned} Kf(z) =\int _{\mathbb {B}_n} k(z, w) f(w) dv(w), \end{aligned}$$
where
......
Corner Boundary Value Problems
Complex Analysis and Operator Theory - Tập 9 - Trang 1157-1210 - 2014
Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro–Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-di......
Growth and Distortion Results for a Class of Biholomorphic Mapping and Extremal Problem with Parametric Representation in $$\mathbb {C}^n$$
Complex Analysis and Operator Theory - Tập 13 - Trang 2747-2769 - 2019
Let
$$\widehat{\mathcal {S}}_g^{\alpha , \beta }(\mathbb {B}^n)$$
be a subclass of normalized biholomorphic mappings defined on the unit ball in
$$\mathbb {C}^n,$$
......
Phase Derivative of Monogenic Signals in Higher Dimensional Spaces
Complex Analysis and Operator Theory - Tập 6 - Trang 987-1010 - 2011
In the Clifford algebra setting of a Euclidean space on the boundary of a domain it is natural to define a monogenic (analytic) signal to be the boundary value of a monogenic (analytic) function inside the domain. The question is how to define a canonical phase and, correspondingly, a phase derivative. In this paper we give an answer to these questions in the unit ball and in the upper-half space.......
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