Linear Operators, Part 2 |
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Page 1823
... Acad . Sci . Paris 222 , 707-709 ( 1946 ) . Remarques sur les racines carrées hermitiennes d'un opérateur hermitien positif borné . C. R. Acad . Sci . Paris 222 , 829–832 ( 1946 ) . Sur la representation spectrale des racines ...
... Acad . Sci . Paris 222 , 707-709 ( 1946 ) . Remarques sur les racines carrées hermitiennes d'un opérateur hermitien positif borné . C. R. Acad . Sci . Paris 222 , 829–832 ( 1946 ) . Sur la representation spectrale des racines ...
Page 1824
... Acad . Tokyo 15 , 169-173 ( 1939 ) . Weak topology , bicompact set and the principle of duality . Proc . Imp . Acad . Tokyo 16 , 63-67 ( 1940 ) . Two fixed - point theorems concerning bicompact convex sets . Proc . Imp . Acad . Tokyo 14 ...
... Acad . Tokyo 15 , 169-173 ( 1939 ) . Weak topology , bicompact set and the principle of duality . Proc . Imp . Acad . Tokyo 16 , 63-67 ( 1940 ) . Two fixed - point theorems concerning bicompact convex sets . Proc . Imp . Acad . Tokyo 14 ...
Page 1845
... Acad . Tokyo 18 , 333-335 ( 1942 ) . Nakamura , M. , and Umegaki , H. 1. A remark on theorems of Stone and Bochner . Proc . Japan Acad . 27 , 506–507 ( 1951 ) . Nakano , H. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Topology and linear ...
... Acad . Tokyo 18 , 333-335 ( 1942 ) . Nakamura , M. , and Umegaki , H. 1. A remark on theorems of Stone and Bochner . Proc . Japan Acad . 27 , 506–507 ( 1951 ) . Nakano , H. 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . Topology and linear ...
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 domain 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 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 subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero