Spectral Theory in Hilbert Space

Bibliography
1. Christer Bennewitz, Symmetric relations on a Hilbert space, In Conference on the
Theory of Ordinary and Partial Differential Equations (Univ. Dundee, Dundee,
1972), pages 212–218. Lecture Notes in Math., Vol. 280, Berlin, 1972. Springer.
2. , Spectral theory for pairs of differential operators, Ark. Mat. 15(1):33–61,
1977.
3. , Spectral asymptotics for Sturm-Liouville equations, Proc. London Math.
Soc. (3) 59 (1989), no. 2, 294–338. MR 91b:34141
4. , A uniqueness theorem in inverse spectral theory, Lecture at the 1997
Birman symposium in Stockholm. Unpublished, 1997.
5. , Two theorems in inverse spectral theory, Preprints in Mathematical
Sciences 2000:15, Lund University, 2000.
6. , A proof of the local Borg-Marchenko theorem, Comm. Math. Phys. 218
(2001), no. 1, 131–132. MR 2001m:34035
7. , A Paley-Wiener theorem with applications to inverse spectral theory,
Advances in differential equations and mathematical physics (Birmingham, AL,
2002), Contemp. Math., vol. 327, Amer. Math. Soc., Providence, RI, 2003,
pp. 21–31. MR 1 991 529
8. G. Borg, Uniqueness theorems in the spectral theory of y ′′ +(λ−q(x))y = 0, Proc.
11th Scandinavian Congress of Mathematicians (Oslo), Johan Grundt Tanums
Forlag, 1952, pp. 276–287.
9. I. M. Gelfand and B. M. Levitan, On the determination of a differential equation
from its spectral function, Izv. Akad. Nauk SSSR 15 (1951), 309–360, English
transl. in Amer. Math. Soc. Transl. Ser 2,1 (1955), 253-304.
10. V. A. Marčenko, Some questions in the theory of one-dimensional second-order
linear differential operators. I, Trudy Moskov. Mat. Obˇsč. 1 (1952), 327–340,
Also in Amer. Math. Soc. Transl. (2) 101, 1-104, (1973).
11. B. Simon, A new approach to inverse spectral theory, I. fundamental formalism,
Annals of Math. 150 (1999), 1–29.
12. H. Weyl. Über gewöhnliche Differentialgleichungen mit Singularitäten und die
zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann., 68:220–269,
1910.
133