Linear Operators, Part 2 |
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Page 1178
... valued functions into the space La ( 2 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , K maps the space L of scalar - valued functions boundedly into the space L ( 2 ) ...
... valued functions into the space La ( 2 ) of square - integrable vector - valued functions . Corollary 19 and Corollary 17 now imply that , for 1 < p < 2 , K maps the space L of scalar - valued functions boundedly into the space L ( 2 ) ...
Page 1179
... valued function with the Fourier transform f ( ) into the vector - valued function whose nth component has the Fourier transform fn ( § ) defined by ( 65 ) fn ( E ) = f ( E ) , 2 " ≤ § < 2n + 1 , = = 0 , otherwise , is a bounded map of ...
... valued function with the Fourier transform f ( ) into the vector - valued function whose nth component has the Fourier transform fn ( § ) defined by ( 65 ) fn ( E ) = f ( E ) , 2 " ≤ § < 2n + 1 , = = 0 , otherwise , is a bounded map of ...
Page 1918
... valued function , ( 196 ) for vector - valued integrals , III.11.17 ( 198 ) Resolution of the identity , X.I ( 889 ) formula for , X.6.1 ( 920 ) , XII.2.10 ( 1202 ) for a normal operator , X.2.5 ( 898 ) for an unbounded operator , XII ...
... valued function , ( 196 ) for vector - valued integrals , III.11.17 ( 198 ) Resolution of the identity , X.I ( 889 ) formula for , X.6.1 ( 920 ) , XII.2.10 ( 1202 ) for a normal operator , X.2.5 ( 898 ) for an unbounded operator , XII ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero