Linear Operators: Spectral theory |
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Page 1290
... coefficients p are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use ...
... coefficients p are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) p ( t ) } ( d / dt ) " is formally self adjoint provided that p ( t ) is a real function . If we use ...
Page 1486
... coefficients a , are periodic and have the same period . We can assume without loss of generality that this period is 1 ; thus a , ( t + 1 ) = a , ( t ) , j = 0 , . . . , n . If follows immediately that all the coefficients of 7 are ...
... coefficients a , are periodic and have the same period . We can assume without loss of generality that this period is 1 ; thus a , ( t + 1 ) = a , ( t ) , j = 0 , . . . , n . If follows immediately that all the coefficients of 7 are ...
Page 1730
... coefficients belonging to C ( R ) , we may state the following analogue of the Gårding inequality , Lemma 10. As to its proof , we need only remark that since , as has been pointed out above , only the points { 0 } × C1 and { 27 } C1 ...
... coefficients belonging to C ( R ) , we may state the following analogue of the Gårding inequality , Lemma 10. As to its proof , we need only remark that since , as has been pointed out above , only the points { 0 } × C1 and { 27 } C1 ...
Contents
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