Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1290
... coefficients pi 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 pi 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 k " ) , ... , k ) , e ,, c1 ) , c ( 2 ) , . ( 1 ) can be determined by formally substituting the asymptotic expression for σ , in [ ** ] and comparing coefficients of z- " . " ... Thus , in all cases in which we deal with a ...
... coefficients k " ) , ... , k ) , e ,, c1 ) , c ( 2 ) , . ( 1 ) can be determined by formally substituting the asymptotic expression for σ , in [ ** ] and comparing coefficients of z- " . " ... Thus , in all cases in which we deal with a ...
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 . are bounded ; If follows immediately that all the ...
... 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 . are bounded ; If follows immediately that all the ...
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