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Progress in Inverse Spectral Geometry (Hardcover, 1997 ed.) Loot Price: R1,639
Discovery Miles 16 390
Progress in Inverse Spectral Geometry (Hardcover, 1997 ed.): Stig I. Andersson, Michel L Lapidus

Progress in Inverse Spectral Geometry (Hardcover, 1997 ed.)

Stig I. Andersson, Michel L Lapidus

Series: Trends in Mathematics

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Loot Price R1,639 Discovery Miles 16 390 | Repayment Terms: R154 pm x 12*

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most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are A-P-S] and Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation' (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e-; namely, u(., t) = V(t)uoU. Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* (r)E), locally given by 00 K(x, y; t) = L>-IAk( k (r) 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2:: >- k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op."

General

Imprint: Birkhauser Verlag AG
Country of origin: Switzerland
Series: Trends in Mathematics
Release date: 2001
First published: 1997
Authors: Stig I. Andersson • Michel L Lapidus
Dimensions: 235 x 155 x 12mm (L x W x T)
Format: Hardcover
Pages: 197
Edition: 1997 ed.
ISBN-13: 978-3-7643-5755-9
Categories: Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry
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LSN: 3-7643-5755-X
Barcode: 9783764357559

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