Linear Operators, Part 2 |
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Page 993
... subset of R with compact closure . Then it follows from what has just been demonstrated that av , ay , i.e. , ap is ... compact closure we have ( i ) · τοτχν = χν · Since every compact set in R is contained in an open set with compact ...
... subset of R with compact closure . Then it follows from what has just been demonstrated that av , ay , i.e. , ap is ... compact closure we have ( i ) · τοτχν = χν · Since every compact set in R is contained in an open set with compact ...
Page 1650
... compact subset of UI outside of which o vanishes . Using Lemma 2.4 , let { 1 , ... , 9 , } be a finite set of functions in Co ° ( E " ) such that o 199 , and such that each = function ዋ vanishes outside some set I. Then p F ( 9 ) = Σ F ...
... compact subset of UI outside of which o vanishes . Using Lemma 2.4 , let { 1 , ... , 9 , } be a finite set of functions in Co ° ( E " ) such that o 199 , and such that each = function ዋ vanishes outside some set I. Then p F ( 9 ) = Σ F ...
Page 1669
... compact subset of I , whenever C is a compact subset of 12 ; Then ( b ) ( M ( · ) ) ; € C∞ ( I1 ) , j 1 , • . , nq . ( i ) for each in C∞ ( I2 ) , q ○ M will denote the function y in C ( I ) defined , for x in I1 , by the equation y ...
... compact subset of I , whenever C is a compact subset of 12 ; Then ( b ) ( M ( · ) ) ; € C∞ ( I1 ) , j 1 , • . , nq . ( i ) for each in C∞ ( I2 ) , q ○ M will denote the function y in C ( I ) defined , for x in I1 , by the equation y ...
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