Linear Operators, Part 2 |
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Page 1403
... neighborhood 40 such that W ( , 2 ) e L2 ( a , c ) for u , -almost all 24 , since A may then be written as a countable union of such neighborhoods 4. We shall show below that for each λe there exists a neighborhood A。 of 2 , an integer ...
... neighborhood 40 such that W ( , 2 ) e L2 ( a , c ) for u , -almost all 24 , since A may then be written as a countable union of such neighborhoods 4. We shall show below that for each λe there exists a neighborhood A。 of 2 , an integer ...
Page 1656
... neighborhood Um , and such that M m = 19m ( x ) = 1 identically for x in a neighborhood of I. Then FΣM - 1 FmPm , and we have only to show that Fmm H ( I ) for each m = 1 , . . . , M. That is ( cf. Lemma 13 ( iv ) ) we may and shall ...
... neighborhood Um , and such that M m = 19m ( x ) = 1 identically for x in a neighborhood of I. Then FΣM - 1 FmPm , and we have only to show that Fmm H ( I ) for each m = 1 , . . . , M. That is ( cf. Lemma 13 ( iv ) ) we may and shall ...
Page 1733
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . 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 . 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I of Euclidean n ...
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 domain 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma 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