Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 ...
Page 1705
... partial differential operator of order at most p - 1 . It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( foS1 ) = fe , that the distribution f satisfies the partial differential equation ( 2 ) Σaj ( εx ) ...
... partial differential operator of order at most p - 1 . It follows from ( 1 ) , from Lemmas 3.22 , 3.18 and 3.6 ( iv ) , and on placing ( foS1 ) = fe , that the distribution f satisfies the partial differential equation ( 2 ) Σaj ( εx ) ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero