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On the spectral Nevanlinna-Pick problem

Constantin Costara (2005)

Studia Mathematica

We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...

Pick-Nevanlinna interpolation on finitely-connected domains

Stephen Fisher (1992)

Studia Mathematica

Let Ω be a domain in the complex plane bounded by m+1 disjoint, analytic simple closed curves and let z 0 , . . . , z n be n+1 distinct points in Ω. We show that for each (n+1)-tuple ( w 0 , . . . , w n ) of complex numbers, there is a unique analytic function B such that: (a) B is continuous on the closure of Ω and has constant modulus on each component of the boundary of Ω; (b) B has n or fewer zeros in Ω; and (c) B ( z j ) = w j , 0 ≤ j ≤ n.

Restricted interpolation by meromorphic inner functions

Alexei Poltoratski, Rishika Rupam (2016)

Concrete Operators

Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions

Paweł Domański, Mikael Lindström (2002)

Annales Polonici Mathematici

We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.

Stieltjes moment problem in general Gelfand-Shilov spaces

Alberto Lastra, Javier Sanz (2009)

Studia Mathematica

The Stieltjes moment problem is studied in the framework of general Gelfand-Shilov spaces, subspaces of the space of rapidly decreasing smooth complex functions, which are defined by imposing suitable bounds on their elements in terms of a given sequence M. Necessary and sufficient conditions on M are stated for the problem to have a solution, sometimes coming with linear continuous right inverses of the moment map, sending a function to the sequence of its moments. On the way, some results on the...

The Dirichlet space: a survey.

Arcozzi, Nicola, Rochberg, Richard, Sawyer, Eric T., Wick, Brett D. (2011)

The New York Journal of Mathematics [electronic only]

Ultraconvergence et singularités pour une classe de séries d'exponentielles

Maurice Blambert, R. Parvatham (1979)

Annales de l'institut Fourier

Localisation des singularités des fonctions analytiques définies par des séries du type Σ P n ( s ) exp ( - s λ n , où les λ n sont complexes et où les P n ( s ) sont des polynômes tayloriens, en utilisant des propriétés obtenues selon deux méthodes originellement dues l’une à B. Lepson pour les séries d’exponentielles à coefficients polynomiaux et dont la suite des exposants est une D -suite et l’autre à G. L. Luntz pour les séries de Taylor-Dirichlet. Le résultat fondamental utilise un théorème de A. F. Leont’ev-G. P. Lapin...

Uniform controllability for the beam equation with vanishing structural damping

Ioan Florin Bugariu (2014)

Czechoslovak Mathematical Journal

This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter ε ∈ ( 0 , 1 ) . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls v ε as ε goes to zero. It is shown that for any time T sufficiently large but independent of ε and for each initial data in a suitable space there exists a uniformly bounded...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Currently displaying 61 – 80 of 118