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A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the…

High Energy Physics - Theory · Physics 2009-10-31 C. G. Carvalhaes , L. V. Belvedere , R. L. P. G. do Amaral , N. A. Lemos

Sarason's Hilbert space version of Carath\'eodory-Julia Theorem connects the non-tangential boundary behavior of functions in de Branges-Rovnyak space $H(b)$ with the existence of angular derivatives in the sense of Carath\'eodory for $b$,…

Functional Analysis · Mathematics 2026-01-06 Shuaibing Luo , Bartosz Malman

We study representations of inner functions on the bidisc from a fractional linear transformation point of view, and provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here…

Functional Analysis · Mathematics 2022-02-08 Ramlal Debnath , Jaydeb Sarkar

In a previous work on the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with…

Analysis of PDEs · Mathematics 2020-10-12 C. Klein , Johannes Sjöstrand , N. Stoilov

Necessary and sufficient conditions for existence of bounded on the entire real axis solutions of Schrodinger equation are obtained under assumption that the homogeneous equation admits an exponential dichotomy on the semi-axes. Bounded…

Dynamical Systems · Mathematics 2012-09-04 A. A. Pokutnyi

We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained…

Complex Variables · Mathematics 2010-11-16 Jan-Fredrik Olsen

We study functional determinants for Dirac operators on manifolds with boundary and discuss the ellipticity of boundary problems by using the Calder\'on projector. We give, for local boundary conditions, an explicit formula relating these…

A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…

Analysis of PDEs · Mathematics 2018-10-25 Andrelino V. Santos , João R. Santos Júnior , Antonio Suárez

We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur properties and norm attainment in the former class of spaces as…

Functional Analysis · Mathematics 2016-07-20 Luis García-Lirola , Colin Petitjean , Abraham Rueda Zoca

The operator-valued Schur-class is defined to be the set of holomorphic functions $S$ mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator…

Classical Analysis and ODEs · Mathematics 2011-11-09 Joseph A. Ball , Animikh Biswas , Quanlei Fang , Sanne ter Horst

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to…

Classical Analysis and ODEs · Mathematics 2011-02-22 Vladimir Derkach , Harry Dym

We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…

Analysis of PDEs · Mathematics 2025-11-05 Evgeny Yu. Panov

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…

Analysis of PDEs · Mathematics 2022-05-10 Kirill D. Cherednichenko , Alexander V. Kiselev , Luis O. Silva

A seminal result of Agler proves that the natural de Branges-Rovnyak kernel function associated to a bounded analytic function on the bidisk can be decomposed into two shift-invariant pieces. Agler's decomposition is non-constructive-a…

Functional Analysis · Mathematics 2017-01-20 Kelly Bickel , Greg Knese

A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud., 4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc…

Complex Variables · Mathematics 2017-05-30 A. I. Bandura , N. V. Petrechko , O. B. Skaskiv

We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath\'eodory and the weaker property of angle preservation - in…

Complex Variables · Mathematics 2024-10-21 Pavel Gumenyuk , Maria Kourou , Annika Moucha , Oliver Roth

Let $\mathfrak M$ and $\mathfrak N$ be separable Hilbert spaces and let $\Theta(\lambda)$ be a function from the Schur class ${\bf S}(\mathfrak M,\mathfrak N)$ of contractive functions holomorphic on the unit disk. The operator…

Functional Analysis · Mathematics 2008-08-19 Yury Arlinskii

If $\ph$ is an analytic function bounded by 1 on the bidisk $\D^2$ and $\tau\in\tb$ is a point at which $\ph$ has an angular gradient $\nabla\ph(\tau)$ then $\nabla\ph(\la) \to \nabla\ph(\tau)$ as $\la\to\tau$ nontangentially in $\D^2$.…

Complex Variables · Mathematics 2010-02-22 Jim Agler , John E. McCarthy , Nicholas J. Young

The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\"ucker coordinate coefficients…

Mathematical Physics · Physics 2013-04-08 V. Enolski , J. Harnad

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…

Functional Analysis · Mathematics 2013-02-21 Marcin Bownik , John Jasper