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 T € 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 ...
... real numbers as a subclass of the class of all complex numbers . In particular , every T € 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 ...
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 ∞ m2 = √ __ 。 t " , μ ( dt ) , √∞∞。 n n 2 maj ...
... 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 ∞ m2 = √ __ 。 t " , μ ( dt ) , √∞∞。 n n 2 maj ...
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 ( λ ...
... 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 ( λ ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero