Band asymptotics in two dimensions
Copyright policy )Band asymptotics in two dimensions
Let X be a rank one symmetric space (e.g., S”, RP”, CP”,...) and let A be its Laplace-Beltrami operator. It is known that the spectrum of A is discrete and consists of a sequence of eigenvalues a, = k(k + a), k = 0, 1, 2 ,a.., (1.1) each occurring with multiplicity N, = (b/(n l)!) k”-’ + O(k”-*), (1.2) n being the dimension of X and a and b being positive integers which depend only on X. Let Q be a zeroth order self-adjoint pseudodifferential operator. If we perturb A by adding Q to it, the eigenvalues (1.1) break up into bands
- Massachusetts Institute of Technology United States
Mathematics(all), Asymptotic distributions of eigenvalues in context of PDEs, Spectral problems; spectral geometry; scattering theory on manifolds, Pseudodifferential operators as generalizations of partial differential operators, measures on the bands of spectral values, Estimates of eigenvalues in context of PDEs, Global Riemannian geometry, including pinching, Morse lemma for volume preserving maps, perturbing the Laplace-Beltrami operator on the 2-sphere or the projective plane by zero order selfadjoint pseudodifferential operators, band asymptotics, Pseudodifferential and Fourier integral operators on manifolds, functional operations in the ring of pseudodifferential operators, averaging lemma, band invariant, Spectral theory; eigenvalue problems on manifolds, spectral asymptotics
Mathematics(all), Asymptotic distributions of eigenvalues in context of PDEs, Spectral problems; spectral geometry; scattering theory on manifolds, Pseudodifferential operators as generalizations of partial differential operators, measures on the bands of spectral values, Estimates of eigenvalues in context of PDEs, Global Riemannian geometry, including pinching, Morse lemma for volume preserving maps, perturbing the Laplace-Beltrami operator on the 2-sphere or the projective plane by zero order selfadjoint pseudodifferential operators, band asymptotics, Pseudodifferential and Fourier integral operators on manifolds, functional operations in the ring of pseudodifferential operators, averaging lemma, band invariant, Spectral theory; eigenvalue problems on manifolds, spectral asymptotics
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