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  1. Bulletin of the Brazilian Mathematical Society
  2. Bulletin of the Brazilian Mathematical Society : Volume 44
  3. Bulletin of the Brazilian Mathematical Society : Volume 44, Issue 4, December 2013
  4. Singular soliton operators and indefinite metrics
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Bulletin of the Brazilian Mathematical Society : Volume 48
Bulletin of the Brazilian Mathematical Society : Volume 47
Bulletin of the Brazilian Mathematical Society : Volume 46
Bulletin of the Brazilian Mathematical Society : Volume 45
Bulletin of the Brazilian Mathematical Society : Volume 44
Bulletin of the Brazilian Mathematical Society : Volume 44, Issue 4, December 2013
Foreword
On scaling limits and Brownian interlacements
The Maslov cycle as a Legendre singularity and projection of a wavefront set
On rigidity of critical circle maps
The equivalence of viscosity and distributional subsolutions for convex subequations — a strong Bellman principle
Quelques problèmes en géométrie feuilletée pour les 60 années de l’IMPA
Min-max theory, Willmore conjecture and the energy of links
Lie groupoids and the Frölicher-Nijenhuis bracket
Foliations with vanishing Chern classes
The homogenization of surfaces and boundaries
Existence and geometric structure of metrics on surfaces which extremize eigenvalues
Singular soliton operators and indefinite metrics
On recurrence and transience of self-interacting random walks
Bulletin of the Brazilian Mathematical Society : Volume 44, Issue 3, September 2013
Bulletin of the Brazilian Mathematical Society : Volume 44, Issue 2, June 2013
Bulletin of the Brazilian Mathematical Society : Volume 44, Issue 1, March 2013
Bulletin of the Brazilian Mathematical Society : Volume 43
Bulletin of the Brazilian Mathematical Society : Volume 42
Bulletin of the Brazilian Mathematical Society : Volume 41
Bulletin of the Brazilian Mathematical Society : Volume 40
Bulletin of the Brazilian Mathematical Society : Volume 39
Bulletin of the Brazilian Mathematical Society : Volume 38
Bulletin of the Brazilian Mathematical Society : Volume 37
Bulletin of the Brazilian Mathematical Society : Volume 36
Bulletin of the Brazilian Mathematical Society : Volume 35
Bulletin of the Brazilian Mathematical Society : Volume 34
Bulletin of the Brazilian Mathematical Society : Volume 33
Bulletin of the Brazilian Mathematical Society : Volume 32
Bulletin of the Brazilian Mathematical Society : Volume 31
Bulletin of the Brazilian Mathematical Society : Volume 30
Bulletin of the Brazilian Mathematical Society : Volume 29
Bulletin of the Brazilian Mathematical Society : Volume 28

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Singular soliton operators and indefinite metrics

Content Provider SpringerLink
Author vikov, Sergey P. Grinevich, Petr G.
Copyright Year 2013
Abstract We consider singular real second order 1D Schrödinger operators such that all local solutions to the eigenvalue problems are x-meromorphic for all λ. All algebrogeometrical potentials (i.e. “singular finite-gap” and “singular solitons”) satisfy to this condition. A Spectral Theory is constructed for the periodic and rapidly decreasing potentials in the classes of functionswith singularities: The corresponding operators are symmetric with respect to some natural indefinite inner product as it was discovered by the present authors. It has a finite number of negative squares in the both (periodic and rapidly decreasing) cases. The time dynamics provided by the KdV hierarchy preserves this number. The right analog of Fourier Transform on Riemann Surfaces with good multiplicative properties (the R-Fourier Transform) is a partial case of this theory. The potential has a pole in this case at x = 0 with asymptotics u ∼ g(g + 1)/x 2. Here g is the genus of spectral curve.
Ending Page 840
Page Count 32
Starting Page 809
File Format PDF
ISSN 16787544
e-ISSN 16787714
Journal Bulletin of the Brazilian Mathematical Society
Issue Number 4
Volume Number 44
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2013-12-14
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword singular finite-gap potentials Operators on spaces with an indefinite metric Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions Theoretical, Mathematical and Computational Physics Particular operators (Dirac, one-dimensional Schrödinger, etc.) Mathematics Symmetric and selfadjoint operators (unbounded) Ordinary differential operators Pontryagin-Sobolev spaces indefinite inner product singular Schrodinger operator Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) Lamé, Mathieu, and spheroidal wave functions
Content Type Text
Resource Type Article
Subject Mathematics
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