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- Andersson, Anders
(författare)
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On the curvature of an inner curve in a Schwarz-Christoffel mapping
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded. In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-Christoffel mapping from R, the unit disk or upper halfplane, to a polygonal region P of a curve inside R. From the Schwarz-Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.
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- Toft, Joachim, 1964-
(författare)
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Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus
- 2002
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Ingår i: Bulletin des Sciences Mathématiques. - PARIS : Elsevier. - 0007-4497 .- 1952-4773. ; 126:2, s. 115-142
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Tidskriftsartikel (refereegranskat)abstract
- We study continuity properties for a family {sp}p1 of increasing Banach algebras under the twisted convolution, which also satisfies that asp, if and only if the Weyl operator aw(x,D) is a Schatten–von Neumann operator of order p on L2. We discuss inclusion relations between the sp-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f(a)s1, when as1 and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.
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