Linear Operators: Spectral theory |
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Page 1540
... essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal differential operator on an interval I , and let B be a linear operator in L2 ( I ) defined in D ( T1 ( 7 ) ) which ...
... essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( 7 ) + B . All Let be a regular formal differential operator on an interval I , and let B be a linear operator in L2 ( I ) defined in D ( T1 ( 7 ) ) which ...
Page 1600
Nelson Dunford, Jacob T. Schwartz. meets the essential spectrum of 7 ( Hartman and Putnam [ 2 ] ) . ( 36 ) Suppose the function q is twice differentiable , and let ( 2 , u ) be an open interval which does not meet the essential spectrum ...
Nelson Dunford, Jacob T. Schwartz. meets the essential spectrum of 7 ( Hartman and Putnam [ 2 ] ) . ( 36 ) Suppose the function q is twice differentiable , and let ( 2 , u ) be an open interval which does not meet the essential spectrum ...
Page 1613
... essential spectrum is to be defined as in Section 6 , and is a closed subset of the complex plane which coincides with the essential spectrum of the formal adjoint operator in the conjugate space . The essential spectrum of a formal ...
... essential spectrum is to be defined as in Section 6 , and is a closed subset of the complex plane which coincides with the essential spectrum of the formal adjoint operator in the conjugate space . The essential spectrum of a formal ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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