Linear Operators, Part 2 |
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Results 1-3 of 87
Page 972
... equal to unity , it follows from Plan- cherel's theorem that { u ( e + p ) } 2 = { u ( e ) } 2 . Hence if u ( e ) << ∞ , we have proved that μ ( e + p ) is also finite and equals u ( e ) . If μ ( e + p ) were known to be finite we ...
... equal to unity , it follows from Plan- cherel's theorem that { u ( e + p ) } 2 = { u ( e ) } 2 . Hence if u ( e ) << ∞ , we have proved that μ ( e + p ) is also finite and equals u ( e ) . If μ ( e + p ) were known to be finite we ...
Page 1539
... equal deficiency indices , and let λ be a real number . Prove that the distance from 2 to the essential spectrum of t is less than or equal to K if and only if there exists a sequence f2 in D ( To ( T ) ) such that f2 = 1 , fn vanishes ...
... equal deficiency indices , and let λ be a real number . Prove that the distance from 2 to the essential spectrum of t is less than or equal to K if and only if there exists a sequence f2 in D ( To ( T ) ) such that f2 = 1 , fn vanishes ...
Page 1735
... equal to 1 in a neighborhood of p = 0 and identically equal to zero outside the unit sphere in E " . Let § in Co ° ( E " ) be identically equal to 1 in a neighborhood of the unit closed sphere in E " and identically zero outside the ...
... equal to 1 in a neighborhood of p = 0 and identically equal to zero outside the unit sphere in E " . Let § in Co ° ( E " ) be identically equal to 1 in a neighborhood of the unit closed sphere in E " and identically zero outside the ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
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 domain 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 linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero