Linear Operators: Spectral theory |
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Page 902
... finite number of these neighborhoods cover the set 8 , of those complex numbers 2 with || ≤ M and whose distance from σ ( T ) is at least 1 / n . Thus E ( f1 ( 8 ) ) = 0. Since E is countably additive E ( f1 ( p ( T ) ) ) = 0 . Hence ...
... finite number of these neighborhoods cover the set 8 , of those complex numbers 2 with || ≤ M and whose distance from σ ( T ) is at least 1 / n . Thus E ( f1 ( 8 ) ) = 0. Since E is countably additive E ( f1 ( p ( T ) ) ) = 0 . Hence ...
Page 1556
... finite number of zeros . ( Hint : it follows that fo0 ' ( t ) dt < ∞o . Express in terms of N ( t ) and integrate . ) = G16 ( Hartman ) Suppose that the equation f 0 has a solution with a finite number of zeros . Prove that there ...
... finite number of zeros . ( Hint : it follows that fo0 ' ( t ) dt < ∞o . Express in terms of N ( t ) and integrate . ) = G16 ( Hartman ) Suppose that the equation f 0 has a solution with a finite number of zeros . Prove that there ...
Page 1913
... finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o - finite meas- ure spaces , ( 188 ) of infinite number of finite meas- ure spaces , III.11.21 ( 205 ) o - finite , III.5.7 ( 136 ) Metric ( s ) , 1.6.1 ( 18 ) ...
... finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o - finite meas- ure spaces , ( 188 ) of infinite number of finite meas- ure spaces , III.11.21 ( 205 ) o - finite , III.5.7 ( 136 ) Metric ( s ) , 1.6.1 ( 18 ) ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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