Zobacz książki o podobnej tematyce

Więcej informacji o Progress in Inverse Spectral Geometry

• Dane szczegółowe
• Opis
• Ulubione w innej kategorii

Za ten zakup dostaniesz 168 punkty

Opis

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.

Szczegóły książki

Kategoria Książki po angielsku Mathematics & science Mathematics Geometry

• Pełny tytuł: Progress in Inverse Spectral Geometry
• Autor: Stig I. Andersson
• Język: Angielski
• Oprawa: Twarda
• Liczba stron: 197
• EAN: 9783764357559
• ISBN: 376435755X
• ID: 04334449
• Wydawca: Birkhauser Verlag AG
• Waga: 1050 g
• Wymiary: 235 × 155 × 23 mm
• Data wydania: 01. October 1997

Ulubione w innej kategorii

---

---

---