Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 968
... neighborhood of hm . By IV.8.19 the integrable continuous functions on R are dense in L1 ( R ) so there is a continuous function fon R such that f1 < 1 and ( f ) ( m ) 0. Let a = | ( Tf ) ( mo ) so that 0 < a < 1 and let U be a neighborhood ...
... neighborhood of hm . By IV.8.19 the integrable continuous functions on R are dense in L1 ( R ) so there is a continuous function fon R such that f1 < 1 and ( f ) ( m ) 0. Let a = | ( Tf ) ( mo ) so that 0 < a < 1 and let U be a neighborhood ...
Page 1733
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I of Euclidean n ...
... neighborhood of the boundary of a domain with smooth boundary . This is carried out in the next two lemmas . 19 LEMMA . Let o be an elliptic formal partial differential operator of even order 2p , defined in a domain I of Euclidean n ...
Page 1734
... neighborhood of q chosen so small that BU , CE , and so that there exists a mapping o of U1 onto Ф the unit spherical neighborhood V of the origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q - 1 is ...
... neighborhood of q chosen so small that BU , CE , and so that there exists a mapping o of U1 onto Ф the unit spherical neighborhood V of the origin such that ( i ) q is one - to - one , is infinitely often differentiable , and q - 1 is ...
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