De Aller-Bedste Bøger - over 12 mio. danske og engelske bøger
Levering: 1 - 2 hverdage

Progress in Inverse Spectral Geometry

Bag om Progress in Inverse Spectral Geometry

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.

Vis mere
  • Sprog:
  • Engelsk
  • ISBN:
  • 9783034898355
  • Indbinding:
  • Paperback
  • Sideantal:
  • 197
  • Udgivet:
  • 1. oktober 1997
  • Udgave:
  • 11997
  • Størrelse:
  • 235x155x11 mm.
  • Vægt:
  • 332 g.
  • 8-11 hverdage.
  • 6. december 2024

Normalpris

Abonnementspris

- Rabat på køb af fysiske bøger
- 1 valgfrit digitalt ugeblad
- 20 timers lytning og læsning
- Adgang til 70.000+ titler
- Ingen binding

Abonnementet koster 75 kr./md.
Ingen binding og kan opsiges når som helst.

Beskrivelse af Progress in Inverse Spectral Geometry

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.

Brugerbedømmelser af Progress in Inverse Spectral Geometry



Find lignende bøger
Bogen Progress in Inverse Spectral Geometry findes i følgende kategorier: