673 research outputs found
The Schrödinger operator: Perturbation determinants, the spectral shift function, trace identities, and all that
No full textTranslated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 41, No. 3, pp. 60-83, 2007 Original Russian Text Copyright © by D. R. Yafaev Dedicated to the 100th anniversary of the birth of Mark Grigor'evich KreinInternational audienceWe discuss applications of the M. G. Krein theory of the spectral shift function to the multidimensional Schrödinger operator. Specific properties of this function, for example, its high-energy asymptotics are studied. Trace identities are derive
Exponential decay of eigenfunctions of first order systems
No full textPapers from the International Conference on Transport and Spectral Problems in Quantum Mechanics held in honor of Jean-Michel Combes at the Université de Cergy-Pontoise, Cergy-Pontoise, September 4--6, 2006The author studies exponential decay of the eigenfunctions of first-order (matrix) differential operators of the form It is shown that under certain assumptions, the eigenfunctions obey estimates of the type The author emphasizes that these estimates are valid everywhere off the essential spectrum , not just below the minimum of
Lectures on scattering theory
No full textThe first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \\cite{I} and numerous applications in \\cite{RS} and \\cite{Y2}. The last two lectures are based on the recent research of the author
Correction to: Unbounded Hankel Operators and Moment Problems
No full textCorrection to: Unbounded Hankel Operators and Moment Problems (Integral Equations and Operator Theory, (2016), 85, 2, (289-300), 10.1007/s00020-016-2289-y)International audienc
Unbounded Hankel operators and moment problems
No full textA correction to this article is available online at https://doi.org/10.1007/s00020-019-2543-1, hal-02379070v1International audienceWe find necessary and sufficient conditions for a non-negative Hankel quadratic form to admit the closure. We also describe the domain of the corresponding closed form. This allows us to define unbounded non-negative Hankel operators under optimal assumptions on their matrix elements. The results obtained supplement the classical Widom condition for a Hankel operator to be bounded
Saint Dimitri of Rostov and Dostoevsky
No full textAcademic literature until now has ignored the possibility of seeing the roots of Dostoevsky’s idea of a God-bearing people in the Saint Dimitri of Rostov’s conception of the passion bearer. But, on the contrary, obvious parallels between the two permit the author to speak of a deliberate coincidence. On the other hand, the two are divided in their conceptions of the reasons for human sufferin
Spectral theory of differential operators: M. Sh Birman 80th anniversary collection
No full textThis volume is dedicated to Professor M. Sh. Birman in honor of his eightieth birthday. It contains original articles in spectral and scattering theory of differential operators, in particular, Schrodinger operators, and in homogenization theory. All articles are written by members of M. Sh. Birman's research group who are affiliated with different universities all over the world. A specific feature of the majority of the papers is a combination of traditional methods with new modern ideas
Die Herkunft des byzantinischen Familiennamens Λάσκαρις
No full textIn this article, the author suggests a new etymology for the name Laskaris, born by a family that gave Byzantium one of its imperial dynasties. Older hypotheses are examined, especially the generally accepted one according to which Laskaris is a name of Persian origin meaning "warrior." The author suggests Lascaris rather comes from a Arabic word defining a physical feature: "blonde" or "red-haired.REB 62 2004 p. 269-273
Dimitri Theodorides, Die Herkunft des Byzantinischen Familiennamens Αάσκαρις. — Cet article propose une nouvelle étymologie du nom Lascaris, porté par une famille qui donna une dynastie à Byzance. L'auteur reprend les hypothèses proposées, notamment celle qui est généralement admise et qui ferait de Lascaris un nom d'origine perse, signifiant le « guerrier ». L'auteur propose plutôt d'y voir un mot arabe caractérisant un trait physique : le « blond » ou le « roux ».Theodoridis Dimitri. Die Herkunft des byzantinischen Familiennamens Λάσκαρις. In: Revue des études byzantines, tome 62, 2004. pp. 269-273
Radiation conditions and scattering theory for -particle hamiltonians (main ideas of the approach)
No full textON SPECTRAL PROPERTIES OF TRANSLATIONALLY INVARIANT MAGNETIC SCHRÖDINGER OPERATORS
No full textAbstract. We consider a class of translationally invariant magnetic fields such that the corresponding potential has a constant direction. Our goal is to study basic spectral properties of the Schrödinger operator H with such a potential. In particular, we show that the spectrum of H is absolutely continuous and we find its location. Then we study the long-time behaviour of solutions exp(−iHt)f of the time dependent Schrödinger equation. It turnes out that a quantum particle remains localized in the plane orthogonal to the direction of the potential. Its propagation in this direction is determined by group velocities. It is to a some extent similar to a evolution of a one-dimensional free particle but “exits ” to + ∞ and − ∞ might be essentially different. 1
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