Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 74
Page 1297
... set of boundary values . Similarly , a complete set of boundary values at a is a maximal linearly independent set of boundary values at a . 18 LEMMA . If τ is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY VALUES.
... set of boundary values . Similarly , a complete set of boundary values at a is a maximal linearly independent set of boundary values at a . 18 LEMMA . If τ is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY VALUES.
Page 1305
... values at c . If d ' 2 , then t ' , and hence 7 , has two boundary values at b . The end point a can be discussed similarly . = = The following table gives the number of linearly independent solutions XIII.2.29 1305 ADJOINTS AND BOUNDARY ...
... values at c . If d ' 2 , then t ' , and hence 7 , has two boundary values at b . The end point a can be discussed similarly . = = The following table gives the number of linearly independent solutions XIII.2.29 1305 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 , τg ) = C1 ( ƒ ) C2 ( g ) —C2 ( ƒ ) C1 ( g ) + D1 ( ƒ ) 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 , τg ) = C1 ( ƒ ) C2 ( g ) —C2 ( ƒ ) C1 ( g ) + D1 ( ƒ ) D2 ( g ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise 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 isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology unique unitary vanishes vector zero