Linear Operators: Spectral theory |
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Page 1040
... analytic at the point = 0. To show this , note that - ( y2 ( λ ) , x ) = ( 2a E ( Ãm ; T ) * R ( Ã ; T ) * y , x ) ... analytic everywhere in the plane except at the origin . Suppose that this function is also known to be analytic at the ...
... analytic at the point = 0. To show this , note that - ( y2 ( λ ) , x ) = ( 2a E ( Ãm ; T ) * R ( Ã ; T ) * y , x ) ... analytic everywhere in the plane except at the origin . Suppose that this function is also known to be analytic at the ...
Page 1102
... analytic function , it follows that det ( I + zT ) is analytic if -z1o ( T ) . Since by ( a ) det ( I + zT ) is bounded , the singularities are removable and ( b ) is proved . Q.E.D. Remark . Since , by the maximum modulus principle , a ...
... analytic function , it follows that det ( I + zT ) is analytic if -z1o ( T ) . Since by ( a ) det ( I + zT ) is bounded , the singularities are removable and ( b ) is proved . Q.E.D. Remark . Since , by the maximum modulus principle , a ...
Page 1364
... analytic matrix { 9 , Q , ( 2 ) } has a non - vanishing determinant for λe G ( 2 ) . It follows easily that { p , Q , ( ) } has an inverse { P1 , ( 2 ) } analytic for λe G ( 2 ) . Thus N and j = 1 Σ Pis ( 2 ) , Qk ( 2 ) = dik , : бік λε ...
... analytic matrix { 9 , Q , ( 2 ) } has a non - vanishing determinant for λe G ( 2 ) . It follows easily that { p , Q , ( ) } has an inverse { P1 , ( 2 ) } analytic for λe G ( 2 ) . Thus N and j = 1 Σ Pis ( 2 ) , Qk ( 2 ) = dik , : бік λε ...
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BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero