عنوان

Progress in Inverse Spectral Geometry

شابک

9783034889384

شابک

9783034898355

شماره

b406305

عنوان اصلي

Progress in Inverse Spectral Geometry

نام عام مواد

[Book]

نام نخستين پديدآور

edited by Stig I. Andersson, Michel L. Lapidus.

محل نشرو پخش و غیره

Basel :

نام ناشر، پخش کننده و غيره

Imprint: Birkhäuser,

تاریخ نشرو بخش و غیره

1997.

عنوان فروست

Trends in Mathematics

متن يادداشت

Spectral Geometry: An Introduction and Background Material for this Volume -- Geometry Detected by a Finite Part of the Spectrum -- Spectral Geometry on Nilmanifolds -- Upper Bounds for the Poincaré Metric Near a Fractal Boundary -- Construction de Variétés Isospectrales du Théorème de T. Sunada -- Inverse spectral theory for Riemannian foliations and curvature theory -- Computer Graphics and the Eigenfunctions for the Koch Snowflake Drum -- Inverse Spectral Geometry -- Inverse Spectral Geometry on Riemann Surfaces -- Quantum Ergodicity.

بدون عنوان

0

متن يادداشت

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* ®E), locally given by 00 K(x,y; t) = L>-IAk(~k ® '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.

شماره استاندارد بين المللي کتاب و موسيقي

9783034898355

عنوان

Springer eBooks

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Andersson, Stig I.

مستند نام اشخاص تاييد نشده

Lapidus, Michel L.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307161200.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y