Linear Operators: Spectral theory |
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Page 64
... prove that Allah did not make the world? Can we prove that Mohammed did not receive teaching from an angel? Not unless we can prove that Allah doesn't exist. Can we do this? If you think proving God is hard, try disproving God. We can ...
... prove that Allah did not make the world? Can we prove that Mohammed did not receive teaching from an angel? Not unless we can prove that Allah doesn't exist. Can we do this? If you think proving God is hard, try disproving God. We can ...
Page 132
... proving that an event e is common knowledge, we must prove EKe without any extra assumption, but we can recursively use the statement that we are proving in the derivation of cCK(EKe). This apparently circular process must satisfy a ...
... proving that an event e is common knowledge, we must prove EKe without any extra assumption, but we can recursively use the statement that we are proving in the derivation of cCK(EKe). This apparently circular process must satisfy a ...
Page 391
... prove various properties of the measurable functions necessary for the development in HOL of the Lebesgue integral and its properties. Definition 4. The Borel sigma algebra on a space X is the smallest sigma algebra generated by the ...
... prove various properties of the measurable functions necessary for the development in HOL of the Lebesgue integral and its properties. Definition 4. The Borel sigma algebra on a space X is the smallest sigma algebra generated by the ...
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 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 linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero