Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
19.02.1966
E-mail: Keywords: integral geometry;tomography;Radon transform;X-ray transform;two-phase and multiphase flows.
Subject:
A complete solution of the limited angle problem for the exponential Radon transform in $R^2$ was obtaine. An explicit inversion formula was obtaine for reconstruction of a function in $R^n$ from $n$-parameter data of the exponential X-ray transform. The uniqueness of reconstruction of the summable in a band function by its integrals over the circles with the centres at a fixed line was proved. The problem of recovery of a function in $R^n$ from data of the spherical Radon transform was solved for some $n$-parameter families of spheres in $R^n$.
Main publications:
Vosstanovlenie funktsii ot dvukh peremennykh po dannym ee eksponentsalnogo luchevogo preobrazovaniya v sluchae nepolnogo uglovogo diapazona // Uspekhi matematicheskikh nauk, 1994, # 2(49), c. 171–172.
O vosstanovlenii funktsii po dannym ee eksponentsialnogo luchevogo preobrazovaniya na $n$-mernom komplekse pryamykh v $R^n$ // Uspekhi matematicheskikh nauk, 1996, # 3(51), c. 177–178.
Edinstvennost vosstanovleniya summiruemoi v polose funktsii po ee integralam po okruzhnostyam s tsentrami na fiksirovannoi pryamoi // Uspekhi matematicheskikh nauk, 1997, # 4(52), c. 213–214.
Zadacha emissionnoi tomografii s nepolnymi dannymi // Obozrenie prikladnoi i promyshlennoi matematiki, 2000, # 2(7), c. 424–425.
Ob obraschenii sfericheskogo preobrazovaniya Radona // Tez. dokl. Mezhdunarodnoi matematicheskoi konferentsii "Differentsialnye uravneniya i sistemy kompyuternoi algebry", Brest: Izd. Brestsk. gos. un-ta, 2000, c. 75–77.
