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Full-Text Articles in Algebra
Generalized Q-Functions And Dirichlet-To-Neumann Maps For Elliptic Differential Operators, Daniel Alpay, Jussi Behrndt
Generalized Q-Functions And Dirichlet-To-Neumann Maps For Elliptic Differential Operators, Daniel Alpay, Jussi Behrndt
Mathematics, Physics, and Computer Science Faculty Articles and Research
The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized Q-function. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein type formulas for the difference of the resolvents and trace formulas in an H2-framework are obtained.
Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup
Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk.
The Schur Transformation For Nevanlinna Functions: Operator Representations, Resolvent Matrices, And Orthogonal Polynomials, Daniel Alpay, A. Dijksma, H. Langer
The Schur Transformation For Nevanlinna Functions: Operator Representations, Resolvent Matrices, And Orthogonal Polynomials, Daniel Alpay, A. Dijksma, H. Langer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we find a Nevanlinna function np which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and np, by which we …
Krein Systems, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Krein Systems, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich
Mathematics, Physics, and Computer Science Faculty Articles and Research
In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role.
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Engineering Faculty Articles and Research
Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …