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A Survey of Scatter...
A Survey of Scattering Theory on Riemann Surfaces with Applications in Global Analysis and Geometry
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- Schippers, Eric (författare)
- Univ Manitoba, Dept Math, Machray Hall, Winnipeg, MB R3T 2N2, Canada.
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- Staubach, Wolfgang (författare)
- Uppsala universitet,Analys och partiella differentialekvationer
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Univ Manitoba, Dept Math, Machray Hall, Winnipeg, MB R3T 2N2, Canada Analys och partiella differentialekvationer (creator_code:org_t)
- Springer, 2023
- 2023
- Engelska.
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Ingår i: Vietnam Journal of Mathematics. - : Springer. - 2305-221X .- 2305-2228. ; 51:4, s. 911-934
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Abstract
Ämnesord
Stäng
- This paper gives an overview of our work on a scattering theory of one-forms and functions in a system of quasicircles on Riemann surfaces. It is rooted in an "overfare" process which takes a harmonic function on one side of the system of quasicircles to a harmonic function on the other side, with the same boundary values in a certain intrinsic non-tangential sense. This is bounded with respect to Dirichlet energy. If extra cohomological data is specified, one can apply this process to harmonic one-forms, and the resulting "scattering matrix" in terms of the holomorphic and anti-holomorphic components of the one-form is unitary. We describe applications to approximation theory, global analysis of singular integral operators on Riemann surfaces, and a new extension of the classical period map to surfaces of genus g with n boundary curves.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Overfare operator
- Scattering
- Bordered surfaces
- Schiffer operators
- Quasicircles
- Period mapping
- Kahler potential
- Generalized polarizations
- Generalized Grunsky inequalities
- Fredholm index
- Conformally nontangential limits
- Conformal Sobolev spaces
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- ref (ämneskategori)
- for (ämneskategori)
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