We deduce a formula for the trace of a boundary-value problem with unbounded operator coefficient and boundary conditions depending on the parameter.
References
M. Bairamogly, “On the regularized trace of a differential operator of order 2n with unbounded operator coefficient,” Spektr. Teor. Differents. Uravn. Ee Prim., No. 8, 15–40 (1987).
C. Erdal, “The trace formula for a differential operator of fourth order with bounded operator coefficients and two terms,” Turk. J. Math., 28, 231–254 (2004).
V. V. Dubrovskii, “Abstract formulas for the regularized traces of smooth elliptic differential operators defined on compact manifolds,” Differents. Uravn., 27, No. 12, 2164–2166 (1991).
M. S. Almamedov, M. Bairamogly, and V. I. Katanova, “Formulas for the traces of a differential equation of fourth order with unbounded operator coefficients,” Dokl. Akad. Nauk SSSR, 317, No. 3, 521–529 (1991).
V. A. Sadovnichii and V. B. Podol’skii, “Traces of operators,” Usp. Mat. Nauk, 61, No. 5, 89–156 (2006).
V. I. Gorbachuk, “Asymptotics of the eigenvalues of boundary-value problems for differential equations in the space of vector functions,” Ukr. Mat. Zh., 27, No. 5, 657–663 (1975); English translation: Ukr. Math. J., 27, No. 5, 542–546 (1975).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 1, pp. 128–134, January, 2014.
Rights and permissions
About this article
Cite this article
Aslanova, N.M., Bairamogly, M. On Generalized Regularized Trace of a Fourth-Order Differential Operator with Operator Coefficient. Ukr Math J 66, 145–152 (2014). https://doi.org/10.1007/s11253-014-0917-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0917-8