Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 . = = ... 9 18 LEMMA . If τ is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY VALUES.
... boundary values . Similarly , a complete set of boundary values at a is a maximal linearly independent set of boundary values at a . = = ... 9 18 LEMMA . If τ is formally self adjoint , XIII.2.17 1297 ADJOINTS AND BOUNDARY VALUES.
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 , Tg ) - C1 ( ƒ ) С2 ( g ) —С2 ( f ) 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 , Tg ) - C1 ( ƒ ) С2 ( g ) —С2 ( f ) C1 ( g ) + D1 ( ƒ ) D2 ( g ) ...
Page 1471
... boundary values at b , we may find two real boundary values D1 , D2 for T2 at b , such that ( t2f , g ) — ( f , t2g ) = D1 ( ƒ ) D2 ( g ) —D¿ ( ƒ ) D1 ( g ) — F¿ ( f , g ) , ƒ ‚ g = D ( T1 ( t2 ) ) . By Theorem 2.30 and Corollary 2.31 ...
... boundary values at b , we may find two real boundary values D1 , D2 for T2 at b , such that ( t2f , g ) — ( f , t2g ) = D1 ( ƒ ) D2 ( g ) —D¿ ( ƒ ) D1 ( g ) — F¿ ( f , g ) , ƒ ‚ g = D ( T1 ( t2 ) ) . By Theorem 2.30 and Corollary 2.31 ...
Contents
IX | 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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero