Linear Operators, Part 2 |
From inside the book
Results 1-3 of 77
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 1663
... subset I。 of I whose closure is compact and contained in I will be denoted by A ( I ) . 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of I ...
... subset I。 of I whose closure is compact and contained in I will be denoted by A ( I ) . 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of I ...
Page 1669
... 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 ( x ) ...
... 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 ( x ) ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Other editions - View all
Common terms and phrases
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