Linear Operators, Part 2 |
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Page 1678
... neighborhood of K1 . Then pp - p vanishes in a neigh- borhood of KC ( F ) , and vanishes in a neighborhood of C ( F ) -K since o vanishes in the complement of K. Hence pp - p vanishes in a neighborhood of C ( F ) , so that F ( pp ) = F ...
... neighborhood of K1 . Then pp - p vanishes in a neigh- borhood of KC ( F ) , and vanishes in a neighborhood of C ( F ) -K since o vanishes in the complement of K. Hence pp - p vanishes in a neighborhood of C ( F ) , so that F ( pp ) = F ...
Page 1733
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . σ 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I of Euclidean n ...
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . σ 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I of Euclidean n ...
Page 1734
... neighborhood of q chosen so small that BU1CE , and so that there exists a mapping 9 of U1 onto the unit spherical neighborhood V of the origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q1 is ...
... neighborhood of q chosen so small that BU1CE , and so that there exists a mapping 9 of U1 onto the unit spherical neighborhood V of the origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q1 is ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero