Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 961
Proof . If we write y for y ( e ) , then ( f , w ) = ££ } ( 2 ) y ( x ) dx = Sx 1 ( 2–0 ) ¥ ( x ) dx = $ 2F10 – xy ( x ) dx = ( 4 ** ) ( O ) = 01f * ) . Since the operation T ( F ) of convolution by f commutes with Ele ) and since ...
Proof . If we write y for y ( e ) , then ( f , w ) = ££ } ( 2 ) y ( x ) dx = Sx 1 ( 2–0 ) ¥ ( x ) dx = $ 2F10 – xy ( x ) dx = ( 4 ** ) ( O ) = 01f * ) . Since the operation T ( F ) of convolution by f commutes with Ele ) and since ...
Page 1179
Proof . We saw in the course of proving Theorem 25 that the mapping M X which sends a scalar - valued function with the Fourier transform | ( 5 ) into the vector - valued function whose nth component has the Fourier transform in ( 5 ) ...
Proof . We saw in the course of proving Theorem 25 that the mapping M X which sends a scalar - valued function with the Fourier transform | ( 5 ) into the vector - valued function whose nth component has the Fourier transform in ( 5 ) ...
Page 1708
... since p ( x ) = 1 for x in Eyje.it follows from Lemmas 3.9 and 3.23 that the restriction fel E14 belongs to A ( m + P ) ( 1/4 ) . Thus ( cf. 3.48 ) || Eg / 4 belongs to A ( m + P ) ( Ex / 4 ) , and the proof of Lemma 3 is complete .
... since p ( x ) = 1 for x in Eyje.it follows from Lemmas 3.9 and 3.23 that the restriction fel E14 belongs to A ( m + P ) ( 1/4 ) . Thus ( cf. 3.48 ) || Eg / 4 belongs to A ( m + P ) ( Ex / 4 ) , and the proof of Lemma 3 is complete .
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