Linear Operators: Spectral theory |
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Page 906
... real numbers as a subclass of the class of all complex numbers . In particular , every Te B ( § ) can be written uniquely in the form T A + iB , where A and B are Hermitian operators . Clearly , A and B must be given by the formulae = A ...
... real numbers as a subclass of the class of all complex numbers . In particular , every Te B ( § ) can be written uniquely in the form T A + iB , where A and B are Hermitian operators . Clearly , A and B must be given by the formulae = A ...
Page 1251
... real numbers . A necessary and sufficient condition that there exist a non- negative measure u defined on the Borel sets of the real line such that √∞ \ t \ " μ ( dt ) < ∞ and is that mn = · [ tru ( dt ) , n = 0 , 1 , 2 , .... n i ...
... real numbers . A necessary and sufficient condition that there exist a non- negative measure u defined on the Borel sets of the real line such that √∞ \ t \ " μ ( dt ) < ∞ and is that mn = · [ tru ( dt ) , n = 0 , 1 , 2 , .... n i ...
Page 1744
... real numbers without a finite limit point ) is bounded below . This , however , follows imme- diately from Corollary ... real axis and the countable set of real numbers o ( V ) . Then , ( i ) there exists a real number K such that | R ...
... real numbers without a finite limit point ) is bounded below . This , however , follows imme- diately from Corollary ... real axis and the countable set of real numbers o ( V ) . Then , ( i ) there exists a real number K such that | R ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero