Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 79
Page 1083
... Exercise 43 is the space L2 ( S , Σ , μ ) of Exercise 44. Let 4 , ( s , t ) be the kernel of Exercise 44 which represents , in the sense of Exercise 44 , the operator 4 , of Exercise 42. Then the power series ∞ 4 ( s , t ; 2 ) - Σλη Δ ...
... Exercise 43 is the space L2 ( S , Σ , μ ) of Exercise 44. Let 4 , ( s , t ) be the kernel of Exercise 44 which represents , in the sense of Exercise 44 , the operator 4 , of Exercise 42. Then the power series ∞ 4 ( s , t ; 2 ) - Σλη Δ ...
Page 1086
... exercise , in the sense of Exercise 44 . Show , finally , that by choosing A ( s , s ) = 0 for all s in S , we obtain the result of Exercise 46 as a special case of the present result . ( Hint : Generalize the method of Exercise 46 ...
... exercise , in the sense of Exercise 44 . Show , finally , that by choosing A ( s , s ) = 0 for all s in S , we obtain the result of Exercise 46 as a special case of the present result . ( Hint : Generalize the method of Exercise 46 ...
Page 1087
... Exercise 30. ) E. Miscellaneous Exercises 50 ( Halberg ) Let ( S , Σ , μ ) be a σ - finite measure space . Let T be a 1 - parameter family of bounded operators defined in a sub- interval I of the parameter interval 1 ≤ p ≤ ∞ , each ...
... Exercise 30. ) E. Miscellaneous Exercises 50 ( Halberg ) Let ( S , Σ , μ ) be a σ - finite measure space . Let T be a 1 - parameter family of bounded operators defined in a sub- interval I of the parameter interval 1 ≤ p ≤ ∞ , each ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
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