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 1435
... coefficients of 2- ” . Thus , in all cases in which we deal with a formal differential operator on an interval I having coefficients analytic in I and with . poles at the free end points of I , the theory of regular and irregular ...
... coefficients of 2- ” . Thus , in all cases in which we deal with a formal differential operator on an interval I having coefficients analytic in I and with . poles at the free end points of I , the theory of regular and irregular ...
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 ...
Contents
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