Linear Operators: Spectral theory |
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Page 1064
... satisfies the inequality g , IA , fp , where I = Ss 2 ( w ) u ( dw ) . To do this , let { m } be a sequence of odd functions , each infinitely often differentiable in the neighborhood of the unit sphere , such that m ( tx ) = ( x ) , t ...
... satisfies the inequality g , IA , fp , where I = Ss 2 ( w ) u ( dw ) . To do this , let { m } be a sequence of odd functions , each infinitely often differentiable in the neighborhood of the unit sphere , such that m ( tx ) = ( x ) , t ...
Page 1144
... satisfies the inequality | R ( λ ; T ) | = O ( 2 - N ) as → 0 along any of the arcs y . Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 , we obtain the ...
... satisfies the inequality | R ( λ ; T ) | = O ( 2 - N ) as → 0 along any of the arcs y . Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 , we obtain the ...
Page 1316
... satisfies the boundary conditions B * ( f ) = 0 , i = 1 , ... , k * of Lemma 3. Now g coincides with K ( c , · ) in neighborhoods of both a and b , and in view of the remark following Corollary 2.28 we see that K ( c , · ) satisfies the ...
... satisfies the boundary conditions B * ( f ) = 0 , i = 1 , ... , k * of Lemma 3. Now g coincides with K ( c , · ) in neighborhoods of both a and b , and in view of the remark following Corollary 2.28 we see that K ( c , · ) satisfies the ...
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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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero