Linear Operators: Spectral theory |
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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 of z- " . 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 z- " . 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 1505
... coefficients and a regular singularity z with exponents e , and e2 , then the second order equation L'f ' = 0 satisfied by f ' ( z ) = ( ≈ - 20 ) f ( z ) has rational coefficients also . The operator L ' has a regular singularity at zo ...
... coefficients and a regular singularity z with exponents e , and e2 , then the second order equation L'f ' = 0 satisfied by f ' ( z ) = ( ≈ - 20 ) f ( z ) has rational coefficients also . The operator L ' has a regular singularity at zo ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero