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General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Jean Dolbeault, Maria Esteban, Eric Séré (2006)

Journal of the European Mathematical Society

This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

Generalisation of Rellich's Theorem on Perturbation of (Essentially) Selfadjoin Operators.

Rainer Wüst (1971)

Mathematische Zeitschrift

Generalized Analytic and Quasi-Analytic Vectors

Jan Rusinek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

For every sequence (aₙ) of positive real numbers and an operator acting in a Banach space, we introduce the families of (aₙ)-analytic and (aₙ)-quasi-analytic vectors. We prove various properties of these families.

Generalized resolvents and spectrum for a certain class of perturbed symmetric operators.

Hebbeche, A. (2005)

Journal of Applied Mathematics

Global existence for a Riccati equation arising in a boundary control problem for distributed parameters

Franco Flandoli (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.