Some Absolutely Continuous Operators I
Some Absolutely Continuous Operators I
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Sj £ ;0'yj '(-)pi ^^ X -• \:uu .^0^) -^Ui -''ZZj. Q'l iiuXi 4. 2 15 CO (4. 5) llfMB= suplf(x)| + / |f(x)|v;(x)doc . Note that assumptions (4t3) and (4. 4) imply that (4. 6) Iklig < ~ . o We maintain that the perturbation problem -D, W(q) satisfies the conditions of Section 2. More specifically v;e maintain the following: Sub theorem 4. 1 Suppose that the function q satisfies conditions ( 4 . 3 ) * (4. 4) and that the bounded interval [^, ,Cp] does not contain the o poin t or a point eigenvalue of the operator -D + M(q) in Lp. Then the perturbation problem -D, M(q) satisfies condi - tions 1-2-3' [C-] jCpl with reference to the Banach space B, The proof of this subtheorem makes essential use of the representation of the unperturbed resolventt, Specifically setting (4. 7) k(u) = e^'^', v;e have (4. 8) R (z)(x, y) = ik(/i-(x-y)), \/z being defined in the plane cut along the positive real axis and having positive imaginary part, a) Condition 1 . [ C •■ > C ^ 3 » Let [Ci^^o^ ^® ^ closed and bounded interval not containing the point 0.
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To quickly assess the difficulty of the text, read a short excerpt:
Sj £ ;0'yj '(-)pi ^^ X -• \:uu .^0^) -^Ui -''ZZj. Q'l iiuXi 4. 2 15 CO (4. 5) llfMB= suplf(x)| + / |f(x)|v;(x)doc . Note that assumptions (4t3) and (4. 4) imply that (4. 6) Iklig < ~ . o We maintain that the perturbation problem -D, W(q) satisfies the conditions of Section 2. More specifically v;e maintain the following: Sub theorem 4. 1 Suppose that the function q satisfies conditions ( 4 . 3 ) * (4. 4) and that the bounded interval [^, ,Cp] does not contain the o poin t or a point eigenvalue of the operator -D + M(q) in Lp. Then the perturbation problem -D, M(q) satisfies condi - tions 1-2-3' [C-] jCpl with reference to the Banach space B, The proof of this subtheorem makes essential use of the representation of the unperturbed resolventt, Specifically setting (4. 7) k(u) = e^'^', v;e have (4. 8) R (z)(x, y) = ik(/i-(x-y)), \/z being defined in the plane cut along the positive real axis and having positive imaginary part, a) Condition 1 . [ C •■ > C ^ 3 » Let [Ci^^o^ ^® ^ closed and bounded interval not containing the point 0.
What to read after Some Absolutely Continuous Operators I?
You can find similar books in the "Read Also" column, or choose other free books by P a Rejto to read online
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