Levinson formula for perturbed Hill operator. (English. Russian original) Zbl 0573.34022

Theor. Math. Phys. 62, 130-140 (1985); translation from Teor. Mat. Fiz. 62, No. 2, 196-209 (1985).
A ”Levinson series”, generalizing the well-known Levinson formula to the case when there is a periodic potential, is obtained for a one- dimensional perturbed Hill operator. Several relevant lemmas are proved.
Reviewer: V.C.Boffi


34L99 Ordinary differential operators
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[1] N. E. Firsova, Zap. Nauchn. Semin. LOMI,51, 183 (1975).
[2] N. E. Firsova, ?Trace formula for a perturbed Schrödinger operator with periodic potential,? Diploma Thesis [in Russian], Leningrad State University (1971).
[3] N. E. Firsova, Problemy Matem. Fiziki (LGU) No. 7, 162 (1974).
[4] N. E. Firsova, Problemy Matem. Fiziki (LGU), No. 8, 158 (1976).
[5] M. Sh. Birman, Mat. Sb.,55, 125 (1961).
[6] F. S. Rofe-Beketov, Dokl. Akad. Nauk SSSR,156, 515 (1964).
[7] V. A. Marchenko and I. V. Ostrovskii, Mat. Sb.,97, 540 (1975).
[8] V. A. Zheludev, Problemy Matem. Fiziki (LGU), No. 4, 61 (1970).
[9] F. S. Rofe-Beketov, Matem. Fizika i Funkts. Analiz (Khar’kov), No. 19, 158 (1973).
[10] N. E. Firsova, Matem. Zametki,36, No. 5 (1984).
[11] N. E. Firsova, Matem. Zametki,18, 831 (1975).
[12] R. G. Newton, J. Math. Phys.,21, 493 (1980). · Zbl 0446.34029
[13] R. G. Newton, ?Inverse scattering by a local impurity in a periodic potential in one dimension,? Preprint IN 47405. Physics Department, Indiana University Bloomington (1982).
[14] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Vol. 2, Clarendon Press, Oxford (1948). · Zbl 0097.27601
[15] N. E. Firsova, Vestn. Leningr. Univ. Ser. Fiz., No. 10/2, 13 (1979).
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