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Page 1629
Nelson Dunford, Jacob T. Schwartz. CHAPTER XIV Linear Partial Differential Equations and Operators 1. Introduction The Cauchy Problem , Local Dependence In this chapter , we shall discuss a variety of theorems having to do with linear ...
Nelson Dunford, Jacob T. Schwartz. CHAPTER XIV Linear Partial Differential Equations and Operators 1. Introduction The Cauchy Problem , Local Dependence In this chapter , we shall discuss a variety of theorems having to do with linear ...
Page 1633
... derivatives not initially required of them . A third category of formal partial differential operators is the parabolic , typified by the operator a a2 θαι θα This sort of operator is closely related to the theory of semi - groups ...
... derivatives not initially required of them . A third category of formal partial differential operators is the parabolic , typified by the operator a a2 θαι θα This sort of operator is closely related to the theory of semi - groups ...
Page 1703
... derivatives , proving the present lemma . Q.E.D. 6. The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it ...
... derivatives , proving the present lemma . Q.E.D. 6. The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to partial differential operators ? In the present section it ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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