Linear Operators: Spectral theory |
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Page 1297
... boundary values . Similarly , a complete set of boundary values at a is a maximal linearly independent set of boundary values at a . = o , j *** 1 , is a 18 LEMMA . If t is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY ...
... boundary values . Similarly , a complete set of boundary values at a is a maximal linearly independent set of boundary values at a . = o , j *** 1 , is a 18 LEMMA . If t is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY ...
Page 1307
Nelson Dunford, Jacob T. Schwartz. boundary values C1 , C2 , D1 , D2 where C1 , C2 are boundary values at a and D1 , D2 are boundary values at b , such that ( tf , g ) — ( f , xg ) = C1 ( ƒ ) C2 ( g ) —C2 ( ƒ ) C1 ( g ) + D1 ( f ) D2 ( g ) ...
Nelson Dunford, Jacob T. Schwartz. boundary values C1 , C2 , D1 , D2 where C1 , C2 are boundary values at a and D1 , D2 are boundary values at b , such that ( tf , g ) — ( f , xg ) = C1 ( ƒ ) C2 ( g ) —C2 ( ƒ ) C1 ( g ) + D1 ( f ) D2 ( g ) ...
Page 1471
... boundary values at b , we may find two real boundary values D1 , D2 for T2 at b , such that 2 2 ( T2f , g ) — ( f , t2g ) = D1 ( ƒ ) D2 ( g ) —D2 ( ƒ ) D1 ( g ) — F , ( f , g ) , f , g = D ( T1 ( t2 ) ) . By Theorem 2.30 and Corollary ...
... boundary values at b , we may find two real boundary values D1 , D2 for T2 at b , such that 2 2 ( T2f , g ) — ( f , t2g ) = D1 ( ƒ ) D2 ( g ) —D2 ( ƒ ) D1 ( g ) — F , ( f , g ) , f , g = D ( T1 ( t2 ) ) . By Theorem 2.30 and Corollary ...
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