Linear Operators: Spectral theory |
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Page 1162
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
... obtained by Wermer [ 7 ] who determined the primary ideals in some of these algebras . Other results of a related nature have been obtained by Beurling [ 2 ] , [ 3 ] . Fredholm theory . Location of eigenvalues . The Fredholm theory of ...
Page 1318
Nelson Dunford, Jacob T. Schwartz. Suppose that the homogeneous system obtained from equations [ 1 ′ ] and [ 2 ′ ] has a non - trivial solution a ( c ) , ( c ) , and let K ( · ) be the function ( of the variable s ) obtained by ...
Nelson Dunford, Jacob T. Schwartz. Suppose that the homogeneous system obtained from equations [ 1 ′ ] and [ 2 ′ ] has a non - trivial solution a ( c ) , ( c ) , and let K ( · ) be the function ( of the variable s ) obtained by ...
Page 1624
... obtained from the operator enjoy the property م cos s√ã cos t√Ãμ ( dλ ) = st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , λ ) by " orthogonalizing " the functions cos tv with ...
... obtained from the operator enjoy the property م cos s√ã cos t√Ãμ ( dλ ) = st . Making use of these relations , Gelfand and Levitan attempt to reconstruct the functions f ( t , λ ) by " orthogonalizing " the functions cos tv with ...
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