enumeration of finite 2-groups; polynomials, the least deviating from zero in L[-1,1] metrics with given number of leading coefficients; the existence`s theorems of functions with certain approximate properties.
Subject:
In a prolongation of researches I. Privaloff, A. Zygmund, S. Lozinskiy, N. Bary and S. Stechkin has put and has decided a task about a complete set of one-dimensional embedding theorems for basic classes of the theory of approximations (switching conjugating), which are characterized by a velocity of decrease of modules of a smoothness or best approximations continuous, and also summable functions in a periodic case. Has received, besides final conditions of concurrence of basic ordinal classes for these functions. Has developed in this connection an original technique of a construction of functions with by the given approximating properties permitting to prove an existence theorem of Bernstein type. After that, being engaged a problem of Zolotarev type about searching polynomials, least deviating from zero, has decided her special case in space $L [-1,1]$ for four ordered higher coefficients. This outcome was obtained by preliminary refinement both development of ideas and approaches available at Korkin and Zolotarev, and also at F. Peherstorfer on the given problem. Within the eightieth years of the last century has found out and has developed one of modes of cataloguing of final 2-groups, which has appeared suitable for enumeration (to within isomorphism) non-Abelian groups with a small index of their center.
Biography
Has ended in 1964 mathematical-mechanical faculty of Ural state university by name A. M. Gor'kiy (Sverdlovsk) also was left there for teaching on faculty of the theory of functions and functional analysis. Has prepared and has protected in 1971 a candidate thesis "Structural and constructive properties of function and her conjugating" (principal the professor L. V. Taykov). A rank of the senior lecturer in 1974. A list of my works contains more than 30 titles.
Main publications:
Geit V. E. Konechnye 2-gruppy stupeni 3 s tsentrom indeksa 8 // Vestnik Chelyabinskogo universiteta. Seriya matematika mekhanika, 1(2), 1994, 162–163.
Geit V. E. O tochnosti nekotorykh neravenstv v teorii priblizhenii // Matem. zametki. 10, 5, 1971, 571–582.
Geit V. E. O strukturnykh i konstruktivnykh svoistvakh funktsii i ee soprzhennoi v $L$ // Izvestiya vuzov. Matematika, 7(122), 1972, 19–30.
Geit V. E. O polinomakh, naimenee uklonyayuschikhsya ot nulya v metrike $L[-1,1]$ // Doklady RAN, 2000, 370, 5, 583–586.
Geit V. E. O polinomakh, naimenee uklonyayuschikhsya ot nulya v metrike $L[-1,1]$ (vtoroe soobschenie) // SibZhVM RAN. Sib. otd-nie. Novosibirsk, 2001. 4, 2, 123–136.
V. È. Gheit, V. V. Gheit, “On polynomials, the least deviating from zero in $L[-1,1]$ metric, with five prescribed coefficients”, Sib. Zh. Vychisl. Mat., 12:1 (2009), 29–40; Num. Anal. Appl., 2:1 (2009), 24–33
V. È. Gheit, N. Zh. Gheit, “Criteria for the constant sign property for real polynomials on a segment”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 11, 80–85; Russian Math. (Iz. VUZ), 52:11 (2008), 70–75
2007
3.
V. È. Gheit, N. Zh. Gheit, “Nonnegativity criteria for fourth degree polynomials on the axis”, Izv. Vyssh. Uchebn. Zaved. Mat., 2007, no. 8, 70–73; Russian Math. (Iz. VUZ), 51:8 (2007), 67–70
2003
4.
V. È. Gheit, “On the polynomials, the least deviating from zero in $L[-1,1]$ metric (third part)”, Sib. Zh. Vychisl. Mat., 6:1 (2003), 37–57
V. È. Gheit, “On functions that are the second modulus of continuity”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 9, 38–41; Russian Math. (Iz. VUZ), 42:9 (1998), 36–38
V. È. Gheit, “The generalized Lorentz theorem on Fourier series with monotone coefficients and its converse”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 4, 15–17; Russian Math. (Iz. VUZ), 42:4 (1998), 12–14
Geit, V. E., “Embedding theorems for Boas classes”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 5, 29–33; Russian Math. (Iz. VUZ), 40:5 (1996), 27–31
12.
V. È. Gheit, N. Zh. Gheit, “О наименьшем уклонении в среднем от нуля
обыкновенных многочленов, неотрицательных на отрезке”, Vestnik Chelyabinsk. Gos. Univ., 1996, no. 3, 43–48
1995
13.
V. È. Geit, “Embedding theorems with respect to $(C,\alpha)$-approximations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 9, 83–84; Russian Math. (Iz. VUZ), 39:9 (1995), 80–81
1994
14.
V. È. Gheit, “Конечные 2-группы ступени 3 с центром индекса 8”, Vestnik Chelyabinsk. Gos. Univ., 1994, no. 2, 162–163
15.
V. È. Gheit, “Конечные 2-группы с центром индекса 4”, Vestnik Chelyabinsk. Gos. Univ., 1994, no. 2, 159–161
1992
16.
V. È. Gheit, “A criterion for satisfying Parseval's equality with a bounded and a summable function”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 7, 9–11; Russian Math. (Iz. VUZ), 36:7 (1992), 7–9
1978
17.
V. È. Gheit, “The absolute convergence of Fourier series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1978, no. 9, 31–36
18.
V. È. Gheit, “Best mean approximation of a cosine series with convex coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1978, no. 8, 50–55; Soviet Math. (Iz. VUZ), 22:8 (1978), 38–42
1974
19.
V. È. Gheit, “Order of $(C,\alpha)$-approximations on certain classes of periodic functions”, Mat. Zametki, 15:1 (1974), 15–20; Math. Notes, 15:1 (1974), 21–32
1973
20.
V. È. Gheit, “The conditions for the imbedding of the classes $H^\omega_{k,\,R}$ и $\widetilde H^\omega_{k,\,R}$”, Mat. Zametki, 13:2 (1973), 169–178; Math. Notes, 13:2 (1973), 101–106
V. È. Gheit, “Structural and constructive properties of sine and cosine series with monotone sequence of Fourier coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1969, no. 7, 39–47
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