Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1797
Amer . J. Math . 78 , 282–288 ( 1956 ) . 4 . On the existence of certain singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . 5 . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6 . Algebras of certain singular ...
Amer . J. Math . 78 , 282–288 ( 1956 ) . 4 . On the existence of certain singular integrals . Acta Math . 88 , 85–139 ( 1952 ) . 5 . On singular integrals . Amer . J. Math . 78 , 289–309 ( 1956 ) . 6 . Algebras of certain singular ...
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Amer . Math . Soc . 39 , 397-400 ( 1933 ) . Harazov , D. F. 1 . On a class of linear equations in Hilbert spaces . Soobščeniya Akad . Sauk Gruzin . SSR 13 , 65–72 ( 1952 ) . ( Russian ) Math . Rev. 14 , 990 ( 1953 2 .
Amer . Math . Soc . 39 , 397-400 ( 1933 ) . Harazov , D. F. 1 . On a class of linear equations in Hilbert spaces . Soobščeniya Akad . Sauk Gruzin . SSR 13 , 65–72 ( 1952 ) . ( Russian ) Math . Rev. 14 , 990 ( 1953 2 .
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Bull . Amer . Math . Soc . 39 , 259–260 ( 1933 ) . 3 . Some theorems on orthogonal functions . Studia Math . 3 , 226–238 ( 1931 ) . Paley , R. E. A. C. , and Wiener , N. 1 . Fourier transforms in the complex domain . Amer . Math . Soc .
Bull . Amer . Math . Soc . 39 , 259–260 ( 1933 ) . 3 . Some theorems on orthogonal functions . Studia Math . 3 , 226–238 ( 1931 ) . Paley , R. E. A. C. , and Wiener , N. 1 . Fourier transforms in the complex domain . Amer . Math . Soc .
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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero