Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 10
Page 1045
... meaning may be assigned to the integral even if fgnk ( x ) | dx = ∞ √gn ei ( z , v ) k ( x ) dx ( for instance , by Plancherel's theorems XI.3.9 and XI.3.22 if fgn k ( x ) 2 dr < ∞ ) , this suggests that we try to define the operator ...
... meaning may be assigned to the integral even if fgnk ( x ) | dx = ∞ √gn ei ( z , v ) k ( x ) dx ( for instance , by Plancherel's theorems XI.3.9 and XI.3.22 if fgn k ( x ) 2 dr < ∞ ) , this suggests that we try to define the operator ...
Page 1185
... meaning for unbounded operators we shall redefine many of these notions in a more general setting . The term operator will be used for a linear map between linear spaces . The symbols D ( T ) and R ( T ) are used for the domain ( or ...
... meaning for unbounded operators we shall redefine many of these notions in a more general setting . The term operator will be used for a linear map between linear spaces . The symbols D ( T ) and R ( T ) are used for the domain ( or ...
Page 1648
... meaning to F for each F in D ( I ) . If , on the other hand , the operator 7 is of order zero , i.e. , is the operation of multiplying by a function a in C ( I ) , then Definition 5 assigns a meaning to the product aF for each F in D ...
... meaning to F for each F in D ( I ) . If , on the other hand , the operator 7 is of order zero , i.e. , is the operation of multiplying by a function a in C ( I ) , then Definition 5 assigns a meaning to the product aF for each F in D ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 other sections not shown
Other editions - View all
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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero