Linear Operators, Part 2 |
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Page 1650
... subset I of E " . Then the closed set Cp in I which is the complement in I of the largest open set in I in which F vanishes , i.e. , which is the complement in I of the union of all the open subsets of I in which F vanishes , is called ...
... subset I of E " . Then the closed set Cp in I which is the complement in I of the largest open set in I in which F vanishes , i.e. , which is the complement in I of the union of all the open subsets of I in which F vanishes , is called ...
Page 1660
... subset of C , in the modified sense explained in the preceding paragraph , then Ca。( I ) will denote the subspace of Ca ( C ) consisting of all functions in Ca ( C ) which vanish outside a compact subset of I. Let I be an open subset ...
... subset of C , in the modified sense explained in the preceding paragraph , then Ca。( I ) will denote the subspace of Ca ( C ) consisting of all functions in Ca ( C ) which vanish outside a compact subset of I. Let I be an open subset ...
Page 1669
... subset of I1 whenever C is a compact subset of I2 ; Then ( b ) ( M ( • ) ) ; € C ( I1 ) , j = 1 , ... , nq . ( i ) for each o in C∞ ( I1⁄2 ) , q ○ M will denote the function Y in C ( I ) defined , for a in I1 , by the equation y ( x ) ...
... subset of I1 whenever C is a compact subset of I2 ; Then ( b ) ( M ( • ) ) ; € C ( I1 ) , j = 1 , ... , nq . ( i ) for each o in C∞ ( I1⁄2 ) , q ○ M will denote the function Y in C ( I ) defined , for a in I1 , by the equation y ( x ) ...
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 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