A Geometric Estimate for a Periodic Schrr Odinger Operator Whose Potential Is the Curvature of a Spherical Curve
نویسندگان
چکیده
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator ?4 d 2 ds 2 + 2 (s) with potential given by the curvature of a closed curve.
منابع مشابه
Absolute Continuity of Periodic Schr odinger
We consider the Schrr odinger operator ? + V in R d with periodic potential V in the Kato class. We show that, if d = 2 or 3, the spectrum of ?+V is purely absolutely continuous.
متن کاملOn Absolute Continuity of the Periodic Schr odinger
This paper concerns the Schrr odinger operator ?+V (x) in R d ; d 3, with periodic potential V. Under the assumption V 2 L d=2 loc (R d), it is shown that the spectrum of ?+V (x) is absolutely continuous. The condition on the potential V is optimal in the context of L p spaces.
متن کاملThe Periodic Schrr Odinger Operators with Potentials in the C. Feeerman-phong Class
We consider the periodic Schrr odinger operator ?+V (x) in R d , d 3 with potential V in the C. Feeerman-Phong class. Let be a periodic cell for V. We show that, for p 2 ((d ? 1)=2; d=2], there exists a positive constant " depending only on the shape of , p and d such that, if lim sup r!0 sup x2 r 2 (1 jB(x; r)j Z B(x;r) jV (y)j p dy) 1=p < "; then the spectrum of ? + V is purely absolutely con...
متن کاملAbsolute Continuity of the Periodicmagnetic Schr Odinger Operatoralexander
We prove that the spectrum of the Schrr odinger operator with periodic electric and magnetic potentials is absolutely continuous.
متن کاملThe Periodic Schr odinger Operators with Potentialsin the C
We consider the periodic Schrr odinger operator ?+V (x) in R d , d 3 with potential V in the C. Feeerman-Phong class. Let be a periodic cell for V. We show that, for p 2 ((d ? 1)=2; d=2], there exists a positive constant " depending only on the shape of , p and d such that, if lim sup r!0 sup x2 r 2
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999