Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 58
Page 1249
... partial isometry . Let x , v M , the initial domain of P. Then the identity | a + v | 2 = | Px + Pv2 shows that ( x ... partial isometry if and only if P * is a partial isometry . 7 THEOREM . If T is a closed transformation whose domain ...
... partial isometry . Let x , v M , the initial domain of P. Then the identity | a + v | 2 = | Px + Pv2 shows that ( x ... partial isometry if and only if P * is a partial isometry . 7 THEOREM . If T is a closed transformation whose domain ...
Page 1629
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
... partial differential operators . Since the theory of linear partial differential operators is vast and highly ramified , we shall only touch upon a number of its aspects , with the intention of displaying a bouquet of applications of ...
Page 1703
... partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial differential operators to be defined below . A crucial theorem in the development of the theory of Chapter ...
... partial differential operators ? In the present section it will be seen that it can , at least for the class of elliptic partial differential operators to be defined below . A crucial theorem in the development of the theory of Chapter ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero