The spectral theory of linear operators, the equations of mathematical physics.
Main publications:
Bobrov A. N. Regulyarizovannye sledy vysshikh poryadkov operatora Laplasa s potentsialom na simmetricheskikh prostranstvakh ranga 1 // Diff. uravneniya, 1997, 33 (6), 800–804.
Bobrov A. N., Podolskii V. E. O skhodimosti sleda stepeni operatora Laplasa–Beltrami s potentsialom na sfere $S^n$ // Funkts. analiz i ego pril., 1997, 31 (4), 69–72.
Bobrov A. N. Sled operatora Laplasa–Beltrami s potentsialom na poverkhnosti Tsollya // Doklady AN, 1999, 368 (2), 154–156.
Bobrov A. N., Podolskii V. E. Skhodimost regulyarizovannykh sledov stepeni operatora Laplasa–Beltrami s potentsialom na sfere $S^n$ // Matem. sbornik, 1999, 190 (10), 3–16.
Bobrov A. N. Spektralnye svoistva nekotorykh dvumernykh kraevykh zadach // Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika. 2001, 1, 3–6.
A. N. Bobrov, “The trace of the Laplace–Beltrami operator with a potential on a Zoll surface”, Differ. Uravn., 35:4 (1999), 528–539; Differ. Equ., 35:4 (1999), 528–539
3.
A. N. Bobrov, V. E. Podolskii, “Convergence of regularized traces of powers of the Laplace–Beltrami operator with potential on the sphere $S^n$”, Mat. Sb., 190:10 (1999), 3–16; Sb. Math., 190:10 (1999), 1401–1415
A. N. Bobrov, “Higher-order regularized traces of the Laplace operator with a potential on symmetric spaces of rank $1$”, Differ. Uravn., 33:6 (1997), 800–804; Differ. Equ., 33:6 (1997), 803–807
A. N. Bobrov, V. E. Podolskii, “On the Convergence of the Trace of a Power of the Laplace–Beltrami Operator with a Potential on the Sphere $S^n$”, Funktsional. Anal. i Prilozhen., 31:4 (1997), 69–72; Funct. Anal. Appl., 31:4 (1997), 280–282
A. N. Bobrov, “Letter to the editors: “The trace of the Laplace-Beltrami operator with a potential on a Zoll surface” [Differ. Uravn. 35 (1999), no. 4, 528–539, 575; MR1719784]”, Differ. Uravn., 35:12 (1999), 1713; Differ. Equ., 35:12 (1999), 1742–2000
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