Linear Operators, Part 2 |
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Page 1092
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
Page 1455
... finite below λ . T 26 COROLLARY . Let τ be a formally symmetric formal differential operator , and let T be any closed symmetric extension ( in particular , any self adjoint extension ) of T。( t ) . Then τ is finite below λ if and only ...
... finite below λ . T 26 COROLLARY . Let τ be a formally symmetric formal differential operator , and let T be any closed symmetric extension ( in particular , any self adjoint extension ) of T。( t ) . Then τ is finite below λ if and only ...
Page 1459
... finite below any finite 2 . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 2 in order to conclude that 7 is finite below 2. But it was shown in the ...
... finite below any finite 2 . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 2 in order to conclude that 7 is finite below 2. But it was shown in the ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero