Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 77
Page 1154
... constant c , ( R ( 2 ) , Σ ( 2 ) , λ ( 2 ) ) = c ( R , Σ , λ ) × ( R , E , λ ) . Since it is clear that ( i ) ( 2 ) ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
... constant c , ( R ( 2 ) , Σ ( 2 ) , λ ( 2 ) ) = c ( R , Σ , λ ) × ( R , E , λ ) . Since it is clear that ( i ) ( 2 ) ... constant c independent of E. This condition ( i ) , as is seen from Corollary III.11.6 , is a consequence of the ...
Page 1176
... constants c , are uniformly bounded . Similarly , multiplying each of the functions k , by a suitable positive constant c ,, we may suppose without loss of generality that each of the functions k , has total variation 1 ; here we have ...
... constants c , are uniformly bounded . Similarly , multiplying each of the functions k , by a suitable positive constant c ,, we may suppose without loss of generality that each of the functions k , has total variation 1 ; here we have ...
Page 1730
... constant A < ∞ fe Co ( C ) . such that ( Tf , g ) ≤ Afg | p ) f , ge Co ( C ) . Now we shall prove an important lemma on elliptic partial differential equations with constant coefficients . 18 LEMMA . Let o be a formal partial ...
... constant A < ∞ fe Co ( C ) . such that ( Tf , g ) ≤ Afg | p ) f , ge Co ( C ) . Now we shall prove an important lemma on elliptic partial differential equations with constant coefficients . 18 LEMMA . Let o be a formal partial ...
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