Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 68
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 1633
... partial differential operator which is negative in this suitable sense , we find ourselves on the common ground of semi - group theory and the theory of parabolic partial differential equations . It should not be supposed that the three ...
... partial differential operator which is negative in this suitable sense , we find ourselves on the common ground of semi - group theory and the theory of parabolic partial differential equations . It should not be supposed that the three ...
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 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 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 Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero