A THIRD ORDER OPERATOR WITH PERIODIC COEFFICIENTS ON THE REAL LINE

作者：Badanin A V^*; Korotyaev E L

来源：St Petersburg Mathematical Journal, 2014, 25(5): 713-734.

DOI：10.1090/S1061-0022-2014-01313-1

• Periodic third order operator
• spectral bands
• spectral asymptotics

The operator i partial derivative(3)+ i partial derivative p+ ip partial derivative+q with 1-periodic coefficients p, q is an element of L-loc(1) (R) is considered on the real line. The following results are obtained: 1) the spectrum of this operator is absolutely continuous, covers the entire real line, and has multiplicity one or three; 2) the spectrum of multiplicity three is bounded and expressed in terms of real zeros of a certain entire function; 3) the Lyapunov function, analytic on a 3-sheeted Riemann surface, is constructed and investigated.

• 出版日期2014-10