Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1040
... analytic at the point = 0. To show this , note that ( y2 ( 2 ) , 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 ( 2 ) , 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 -z - 1o ( 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 ...
... analytic function , it follows that det ( I + zT ) is analytic if -z - 1o ( 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 ...
Page 1364
... analytic matrix { 9 , Q , ( 2 ) } has a non - vanishing determinant for λ € G ( 2 ) . It follows easily that { p , Q , ( ) } has an inverse { P1 , ( 2 ) } analytic for 2e G ( 2 ) . Thus N Σ Pi¿ ( λ ) ; Qx ( 2 ) = dik , 2 € G ( 20 ) , j ...
... analytic matrix { 9 , Q , ( 2 ) } has a non - vanishing determinant for λ € G ( 2 ) . It follows easily that { p , Q , ( ) } has an inverse { P1 , ( 2 ) } analytic for 2e G ( 2 ) . Thus N Σ Pi¿ ( λ ) ; Qx ( 2 ) = dik , 2 € G ( 20 ) , j ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero