Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1309
... condition , which is necessarily a boundary condition at a . It is easily seen from the preceding equation and Definition XII.4.25 that the most general symmetric boundary condition is af ' ( a ) + ßf ( a ) = 0 with a and ẞ real . Thus ...
... condition , which is necessarily a boundary condition at a . It is easily seen from the preceding equation and Definition XII.4.25 that the most general symmetric boundary condition is af ' ( a ) + ßf ( a ) = 0 with a and ẞ real . Thus ...
Page 1310
... condition must be a boundary condition at a . Hence it is clear from the above table that there is exactly one solution y of ( 7-2 ) y = 0 square - integrable at band satisfying all boundary conditions at b , and at least one solution q ...
... condition must be a boundary condition at a . Hence it is clear from the above table that there is exactly one solution y of ( 7-2 ) y = 0 square - integrable at band satisfying all boundary conditions at b , and at least one solution q ...
Page 1471
... condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( 7 ) defined by the boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( f ) = 0 ( if 7 has any boundary values at a ) ...
... condition B ( ƒ ) = 0 ( if has any boundary values at a ) , then S * is the restriction of T1 ( 7 ) defined by the boundary condition f ( t ) + cf ' ( t ) = 0 and by the boundary condition B ( f ) = 0 ( if 7 has any boundary values at a ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero