Linear Operators, Part 2 |
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Page 1245
... fact that each complex number & has a unique representation a α where r≥ 0 , and e1o | 1. By analogy with the fact that r = ( ãα ) , we shall first seek to obtain the self adjoint operator A from the operator T * T . = = reio , 1 LEMMA ...
... fact that each complex number & has a unique representation a α where r≥ 0 , and e1o | 1. By analogy with the fact that r = ( ãα ) , we shall first seek to obtain the self adjoint operator A from the operator T * T . = = reio , 1 LEMMA ...
Page 1348
... fact makes evident what could readily be suspected before : that from the point of view of the negative real axis , a more favorable choice of basis for the solutions of to λσ = is ô ( t , ả ) - ô1⁄2 ( t , 2 ) = et√ - Ã ̧ Το = τσ = Of ...
... fact makes evident what could readily be suspected before : that from the point of view of the negative real axis , a more favorable choice of basis for the solutions of to λσ = is ô ( t , ả ) - ô1⁄2 ( t , 2 ) = et√ - Ã ̧ Το = τσ = Of ...
Page 1750
... fact is needed in the course of the proof of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no boundedness restriction is imposed on the coefficient matrices 4 ,, as the ...
... fact is needed in the course of the proof of Theorem 1 , and shall prove it by a direct method where it is needed . Remark 2. The theorem is false if no boundedness restriction is imposed on the coefficient matrices 4 ,, as 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