Linear Operators, Part 2 |
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Page 1638
... derivatives of order not more than k exists and is continuous . The sets Co ( I ) and C ( I ) consist of those ... derivative has a continuous extension to I. If this is the case , f ( x ) is defined for x in Ĭ and | J | ≤ k as the ...
... derivatives of order not more than k exists and is continuous . The sets Co ( I ) and C ( I ) consist of those ... derivative has a continuous extension to I. If this is the case , f ( x ) is defined for x in Ĭ and | J | ≤ k as the ...
Page 1687
... derivatives of order not more than k belong to L ( E ) . By Lemma 3 , ( h ; F ) oq - 1 and all its derivatives of order not more than m are continuous in the closure of V. From this and Lemma 3.47 it is evident that h¡F ( h , F ) op1op ...
... derivatives of order not more than k belong to L ( E ) . By Lemma 3 , ( h ; F ) oq - 1 and all its derivatives of order not more than m are continuous in the closure of V. From this and Lemma 3.47 it is evident that h¡F ( h , F ) op1op ...
Page 1699
... derivatives of higher order may be introduced , and to discuss a few elementary properties of these notions . 1 DEFINITION . Let I be a domain in E " whose boundary B contains a part Σ which is a smooth surface . Suppose that no point ...
... derivatives of higher order may be introduced , and to discuss a few elementary properties of these notions . 1 DEFINITION . Let I be a domain in E " whose boundary B contains a part Σ which is a smooth surface . Suppose that no point ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 deficiency indices Definition denote dense domain eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero