Linear Operators, Part 2 |
From inside the book
Results 1-3 of 59
Page 1310
... solution y of ( 7-2 ) = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution q of ( 7-2 ) 9 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were a ...
... solution y of ( 7-2 ) = 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution q of ( 7-2 ) 9 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were a ...
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 \ f ...
... 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 \ f ...
Page 1529
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1⁄212 * −1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a ...
... solution whose asymp- totic expansion begins with the factor exp ( ¿ 1⁄212 * −1 ) . Thus , a solution ( " small solution " ) with the first kind of asymptotic expansion is uniquely determined by its asymptotic expansion ; while a ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
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 coefficients compact operator complex numbers constant 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero