Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 54
Page 1472
... solution of tσ = λσ square- integrable at a and satisfying the boundary condition B , so is f . Since , by the preceding lemma , only one such solution ( up to a constant multiple ) exists , we must have ƒ = af , where , since | ƒ ...
... solution of tσ = λσ square- integrable at a and satisfying the boundary condition B , so is f . Since , by the preceding lemma , only one such solution ( up to a constant multiple ) exists , we must have ƒ = af , where , since | ƒ ...
Page 1521
... solution of the order of t - 1 - i as t → ∞ and another which behaves like ti as too . The solution at 20 = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L1 - λ has precisely one solution belonging to L2 ( 2 , ∞ ) for each ...
... solution of the order of t - 1 - i as t → ∞ and another which behaves like ti as too . The solution at 20 = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L1 - λ has precisely one solution belonging to L2 ( 2 , ∞ ) for each ...
Page 1529
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) −1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1 ) −1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a solution ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 other sections not shown
Other editions - View all
Common terms and phrases
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