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Boris Vasil’evich Fedosov (obituary). (English. Russian original) Zbl 1241.01028
Russ. Math. Surv. 67, No. 1, 167-174 (2012); translation from Usp. Mat. Nauk 67, No. 1, 169-176 (2012).
With list of selected publications (29 items).
[1] Asymptotic formulas for the eigenvalues of the Laplace operator in the case of a polyhedron. (English. Russian original) Sov. Math., Dokl. 5, 988–990 (1964); translation from Dokl. Akad. Nauk SSSR 157, 536–538 (1964). Zbl 0133.36101

[2] (with N.V. Kuznetsov) An asymptotic formula for the eigenvalues of a circular membrane, Differ. Equations 1(1965), 1326–1329 (1967); translation from Differ. Uravn. 1, 1682–1685 (1965). (English. Russian original) Zbl 0152.43807

[3] Index of an elliptic system on a manifold. (English. Russian original) Funct. Anal. Appl. 4, 312-320 (1970); translation from Funkts. Anal. Prilozh. 4, No. 4, 5767 (1970). Zbl 0246.58020

[4] Analytic formulas for the index of elliptic operators. (English. Russian original) Trans. Mosc. Math. Soc. 30, 159-240 (1974); translation from Tr. Mosk. Mat. Obshch. 30, 159-241 (1974) Zbl 0349.58006

[5a] An analytic formula for the index of an elliptic boundary-value problem” Math. USSR, Sb. 22(1974), 61-90 (1975); translation from Mat. Sb., N. Ser. 93(135), 62-89 (1974) (English. Russian original) Zbl 0306.58016

[5b] An analytic formula for the index of an elliptic boundary-value problem. Pt. II, Math. USSR, Sb. 24(1974), 511-535 (1976); translation from Mat. Sb., N. Ser. 95(137), 525-550 (1974). (English. Russian original) Zbl 0312.58010

[5c] An analytic formula for the index of an elliptic boundary-value problem. Pt. III, Math. USSR, Sb. 30(1976), 341-359 (1978); translation from Mat. Sb., N. Ser. 101(143), 380-401 (1976) (English. Russian original) Zbl 0349.58007

[6] A periodicity theorem in the algebra of symbols”, Math. USSR, Sb. 34, 382-410 (1978); translation from Mat. Sb., N. Ser. 105(147), 431-462 (1978) (English. Russian original) Zbl 0391.47033

[7a] (with M. A. Shubin) The index of random elliptic operators. I, Math. USSR, Sb. 34, 671-699 (1978); translation from Mat. Sb., N. Ser. 106(148), 108-140 (1978) (English. Russian original) Zbl 0409.47030

[7b] (with M. A. Shubin) The index of random elliptic operators. II, Math. USSR, Sb. 35, 131-156 (1979); translation from Mat. Sb., N. Ser. 106(148), 455-483 (1978) (English. Russian original) Zbl 0392.58010

[8] Formal quantization. (Russian) Some problems in modern mathematics and their applications to problems in mathematical physics (Russian), 129–136, Mosk. Fiz.-Tekhn. Inst., Moscow, 1985. mr=0933154

[9] An index theorem in the algebra of quantum observables. (Russian) Some questions of mathematics in problems of physics and mechanics (Russian), 83–90, Mosk. Fiz.-Tekhn. Inst., Moscow, 1988. mr=1222007

[10] Deformation quantization and asymptotic operator representation. Funct. Anal. Appl. 25, No. 3, 184–194 (1991); translation from Funkts. Anal. Prilozh. 25, No. 3, 24–36 (1991). (English. Russian original) Zbl 0737.47042

[11] Index theorems. Partial differential equations VIII. Encycl. Math. Sci. 65, 155–251 (1996); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 65, 165–268 (1991). (English. Russian original) Zbl 0884.58087

[12] A trace formula for the Schrödinger operator. Russ. J. Math. Phys. 1, No. 4 , 447–463 (1993) Zbl 0909.58053</a>

[13] A simple geometrical construction of deformation quantization. J. Differ. Geom. 40, No. 2, 213–238 (1994) Zbl 0812.53034

[14] Reduction and eigenstates in deformation quantization. Pseudo-differential calculus and mathematical physics, Math. Top., 5, Akademie-Verlag, Berlin, 277–297 (1994) Zbl 0809.58012</a>

[15] F. Golse, E. Leichtnam, and E. Schrohe, The noncommutative residue for manifolds with boundary, J. Funct. Anal. 142, No. 1, 1–31 (1996) Zbl 0877.58005
[16] Deformation quantization and index theory, Math. Top., 9, Akademie-Verlag, Berlin, 1996 Zbl 0867.58061
[17] Non-abelian reduction in deformation quantization. Lett. Math. Phys., 43, No. 2, 137–154 (1998) Zbl 0964.53055
[18] B.-W. Schulze and N. Tarkhanov, The index of elliptic operators on manifolds with conical points, Selecta Math. (N.S.) 5, No. 4, 467–506 (1999) Zbl 0951.58026
[19] Preprint 98/27, Institut für Mathematik, Universität Potsdam, (1998)
http://opus.kobv.de/ubp/volltexte/2008/2539/
[20] The Atiyah-Bott-Patodi method in deformation quantization. Commun. Math. Phys., 209, No. 3, 691–728 (2000) Zbl 0958.58020 doi: 10.1007/s002200050035
[21] On G-trace and G-index in deformation quantization. Lett. Math. Phys. 52, No. 1, 29–49 (2000) Zbl 0998.53058

[22] Pseudo-differential operators and deformation quantization. Quantization of singular symplectic quotients, Prog. Math. 198, Birkhäuser, Basel, 2001, 95–118 Zbl 1026.53052

[23] B.-W. Schulze and N. Tarkhanov, Analytic index formulas for elliptic corner operators. Ann. Inst. Fourier (Grenoble), 52, No. 3 (2002), 899–982 Zbl 1010.58018 doi:10.5802/aif.1906

[24] On the trace density in deformation quantization. Deformation Quantization, Strasbourg 2001, IRMA Lect. Math. Theor. Phys., 1, de Gruyter, Berlin, 2002, 67–83 Zbl 1014.53056

[25] B.-W. Schulze and N. Tarkhanov, On the index theorem for symplectic orbifolds, Ann. Inst. Fourier 54, No. 5 (2004), 1601–1639 Zbl 1071.53055

[26] On a spectral theorem for deformation quantization. Int. J. Geom. Methods Mod. Phys. 3, No. 8 (2006), 1609–1626 Zbl 1108.53045

[27] T. Ispiryan, On perturbations of Morse Hamiltonians. Int. J. Geom. Methods Mod. Phys. 4, No. 8 (2007), 1269–1283 Zbl 1142.53072

[28] Deformation quantization and boundary-value problems, with N. N. Tarkhanov, unfinished

[29] Towards direct proof of the index theorem for deformation quantization, unpublished
MSC:
01A70 Biographies, obituaries, personalia, bibliographies
Biographic References:
Fedosov, Boris Vasil’evich
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