Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
17.06.1935
E-mail: ,
Keywords: spectral theory; non-selfadjoint operators; differential and integral equations; resolvent; eigenvalue-series expansion.
Subject:
Fundamental results were obtained in the spectral theory of non-selfadjoint differential and integral operators: a complete solution of a difficult eigenfunctions expansions problem for ordinary differential operators with nonregular decomposing boundary conditions was found; the eigenfunctions expansions problems for integral operators which are the sum of a Volterra and a finite-dimensional operators in the case of exponential growth of the resolvent and for integral operators which kernels have power behaviour on the diagonals were solved.
Main publications:
Khromov A. P. Razlozhenie po sobstvennym funktsiyam obyknovennykh differentsialnykh operatorov s neregulyarnymi raspadayuschimisya kraevymi usloviyami // Matem. sbornik, 1966, 70 (112), # 3, 310–329.
Khromov A. P. O porozhdayuschikh funktsiyakh volterrovykh operatorov // Matem. sbornik, 1977, 102 (144), # 3, 457–472.
Khromov A. P. Teoriya ravnoskhodimosti dlya integrodifferentsialnykh i integralnykh operatorov // Matem. sbornik, 1981, 114 (156), # 3, 378–405.
Khromov A. P. Asimptotika rezolvent integralnykh volterrovykh operatorov. Trudy MIAN, 1995, 211, 419–442.
Khromov A. P., Kornev V. V. O ravnoskhodimosti razlozhenii po sosbstvennym funktsiyam integralnykh operatorov s yadrami, dopuskayuschimi razryvy proizvodnykh na diagonalyakh // Matem. sbornik, 2001, 192, # 10, 33–50.
Khromov A. P. Konechnomernye vozmuscheniya volterrovykh operatorov // Sovremennaya matematika. Fundamentalnye napravleniya. 2004. T. 10. S. 3–163.
Khromov A. P. Integralnye operatory s yadrami, razryvnymi na lomanykh liniyakh // Matem. sb. 2006. T. 197, vyp. 11. S. 115–142.
Khromov A. P. O ravnoskhodimosti razlozhenii po sobstvennym funktsiyam integralnykh operatorov s peremennymi predelami integrirovaniya // Integralnye preobrazovaniya i spetsialnye funktsii. Informatsionnyi byulleten. T. 6, # 1. 2006. S. 46–55.
Kornev V. V., Khromov A. P. Operator integrirovaniya s involyutsiei v verkhnem predele integrirovaniya // Dokl. AN. 2008. T. 422, # 4. S. 459–462.
Kurdyumov V. P., Khromov A. P. O bazisakh Rissa iz sobstvennykh i prisoedinennykh funktsii funktsionalno-differentsialnogo uravneniya s operatorom otrazheniya // Differentsialnye uravneniya. 2008. T. 44, # 2. S. 196–204.
Burlutskaya M. Sh., Khromov A. P. Klassicheskoe reshenie dlya smeshannoi zadachi s involyutsiei // Dokl. AN. 2010. T. 435, # 2. S.1643–1646.
Burlutskaya M. Sh., Khromov A. P. Teorema Shteingauza o ravnoskhodimosti dlya funktsionalno-differentsialnykh operatorov // Matem. zametki. 2011. T. 90, vyp. 1. S. 22–33.
Burlutskaya M. Sh., Khromov A. P. Metod Fure v smeshannoi zadache dlya uravneniya pervogo poryadka s involyutsiei // ZhVM i MF. 2011. T. 51, # 12. S. 2233–2246.
Burlutskaya M. Sh., Kurdyumov V. P., Khromov A. P. Utochnennye asimptoticheskie formuly dlya sobstvennykh znachenii i sobstvennykh funktsii sistemy Diraka // Dokl. AN. 2012. T. 443, # 4. S. 414–417.
Burlutskaya M. Sh., Khromov A. P. Funktsionalno differentsialnye operatory s involyutsiei i operatory Diraka s periodicheskimi kraevymi usloviyami // Dokl. AN. 2014. T. 454, # 1. S. 15–17.
Burlutskaya M. Sh., Khromov A. P. Rezolventnyi podkhod v metode Fure // Dokl. AN. 2014. T. 458, # 2. S. 138–140.
Kuznetsov N., Khromov A. The Fourier Method in Russia Before and Aster V. A. Steklov // Math. Intelligencer. 2014. Vol. 36, iss. 4. P. 66–73.
Khromov A. P. Smeshannaya zadacha dlya volnovogo uravneniya s proizvolnymi dvukhtochechnymi kraevymi usloviyami // Dokl. AN. 2015. T. 462, # 2. S. 148–150.
Khromov A.P., Kornev V.V. Rezolventnyi podkhod k metodu Fure v odnoi smeshannoi zadache dlya volnovogo uravneniya // Zh. vychisl. matem. i matem. fiz. 2015. T. 55, # 4. S. 621–630.
Khromov A.P., Burlutskaya M.Sh. Rezolventnyi podkhod dlya volnovogo uravneniya // Zh. vychisl. matem. i matem. fiz. 2015. T. 55, # 2. S. 51–63.
Rezolventnyi podkhod v metode Fure dlya volnovogo uravneniya v nesamosopryazhennom sluchae // Zh. vychisl. matem. i matem. fiz. 2015. T. 55, # 7. S. 1156–1167.
Khromov A. P., Kornev V. V. Povedenie formalnogo resheniya smeshannoi zadachi dlya volnovogo uravneniya // Zh. vychisl. matem. i matem. fiz. 2016. T. 56, # 2. S. 239–251.
