The problem of multiple interpolation was formulated and solved in the class of functions of at most normal type for proximate order in the upper half-plane. A theory of sets of regular growth of functions that are analytic in the upper half-plane, relative to a given indicator was developed. A multiple interpolation problem was solved in the class of functions of completely regular growth in the closed upper half-plane which have a prescribed indicator and relative to a given proximal order, as well as in the class of functions analytic in the half-plane which have an indicator that does not exceed a prescribed one. A criterion in the term of Fourier coefficients of delta-subharmonic function was obtained that one is in the class of functions of given growth in the upper half-plane. A number of papers (with N. Sadyk) were devoted to the theory of delta-subharmonic functions of completely regular growth in the upper half-plane.
Main publications:
K. G. Malyutin, “Ryady Fure i $\delta$-subgarmonicheskie funktsii konechnogo $\gamma$-tipa v poluploskosti”, Matem. sb., 192:6 (2001), 51–70
K. G. Malyutin, N. Sadyk, “Predstavlenie subgapmonicheskikh funktsii v poluploskosti
2007. – T. 198, №12. – C. 47–62.”, Matem. sb., 198:12 (2007), 47–62
O. A. Bozhenko, K. G. Malyutin, “Zadacha kratnoi interpolyatsii v klasse analiticheskikh funktsii nulevogo poryadka v poluploskosti”, Ufimsk. matem. zhurn., 6:1 (2014), 18–29
K. G. Malyutin, I.\I. Kozlova, N. Sadyk, “Kanonicheskie funktsii dopustimykh mer v poluploskosti”, Matem. zametki, 96:3 (2014), 418–431
O. A. Bozhenko, A.,F. Grishin, K. G. Malyutin, “Interpolyatsionnaya zadacha v klasse tselykh funktsii nulevogo poryadka”, Izv. RAN. Ser. matem., 79:2 (2015), 21-44
