{"product_id":"9783764357559","title":"Progress in Inverse Spectral Geometry (Trends in Mathematics)","description":"\u003cp\u003emost 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. 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.\u003c\/p\u003e","brand":"Birkhauser","offers":[{"title":"Default Title","offer_id":45484578373711,"sku":"00000_00000_00000_00000","price":1925.0,"currency_code":"TWD","in_stock":false}],"url":"https:\/\/kinokuniya.com.tw\/products\/9783764357559","provider":"Books Kinokuniya Taiwan","version":"1.0","type":"link"}