Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 t 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 t 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 ) D¿ ( 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 ) D¿ ( 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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero