Institute for Mathematical Physics Estimates of Periodic Potentials in Terms of Gap Lengths Estimates of Periodic Potentials in Terms of Gap Lengths Dedicated to My Teacher Mikhail Birman on the Occasion of His 70th Birthday
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چکیده
Deene the Hill operator T = ?d 2 =dx 2 + q(x) in L 2 (R) and suppose q 2 L 2 (0; 1) is a 1-periodic real potential, R 1 0 q(x)dx = 0: We prove the estimate kqk 6 2kk(1 + kk 1=3); where kk 2 = P n>1 j n j 2 and j n j > 0; n > 1; is the gap length of T.
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تاریخ انتشار 1998