Criteria for the unconditional basis property and the Riesz basis property for a system of root functions of an ordinary nonselfadjoint 2m-order differential operator (which are understood in a framework developed by V. A. Il'in, i.e. irrespective of boundary conditions) were established. The criterion for Bessel property in $L_2$ of such systems also was established. As an instrument of researching, a subdivision of a root function system onto classes in terms of relations between there norms in different spaces was proposed. It has been proved that one can modify any system of root functions by means of linear combinations (with eigenfunctions remained valid) so that new system satisfies a posteriory estimation. For extended systems of sines, cosines, exponentials and systems of root functions of 2-order operator, it has been proved that the Bessel and Hilbert properties are stable with respect to small perturbations of spectral parameter.
Biography
Graduated from Faculty of Computational Mathematics and Cybernetics of M. V. Lomonosov Moscow State University (MSU) in 1978 (departement of Common Mathematics). Ph.D. thesis was defended in 1987. D.Sci. thesis was defended in 1993. A list of my works containes about 50 titles.
In 1996–1998 I was a head of reseach project "Basic properties of systems of root functions of nonselfajoint differential operators" (grand of RFBR). In 1999 I was awarded the title Soros' Professor.
Main publications:
Budaev V. D. O neravenstve Besselya dlya sistem kornevykh funktsii differentsialnykh operatorov // Doklady AN SSSR, 1991, 318(1), 16–20.
Budaev V. D. Neobkhodimoe uslovie bazisnosti Rissa sistem kornevykh obyknovennogo nesamosopryazhennogo differentsialnogo operatora // Differentsialnye uravneniya, 1993, 29(1), 20–30.
Budaev V. D. Nekotorye svoistva kornevykh funktsii differentsialnykh operatorov, svyazannye s bezuslovnoi bazisnostyu // Differentsialnye uravneniya, 1996, 32(1), 9–14.
Budaev V. D. O neravenstvakh Gilberta i Besselya dlya nekotorykh sistem funktsii // Doklady Akademii nauk, 1997, 357(2), 157–160.
V. D. Budaev, O. V. Kolesnikova, “On the relationship between the Carleman condition and the equivalence of norms of root functions on various compact sets”, Differ. Uravn., 42:4 (2006), 441–447; Differ. Equ., 42:4 (2006), 465–472
2001
2.
V. D. Budaev, “The Gap Lengths in the Sequence of Spectral Parameters of Hilbert Function Systems”, Differ. Uravn., 37:2 (2001), 164–170; Differ. Equ., 37:2 (2001), 178–184
2000
3.
V. D. Budaev, “The Hilbert inequality for a one-parameter family of functions”, Differ. Uravn., 36:7 (2000), 996–997; Differ. Equ., 36:7 (2000), 1106–1108
4.
N. V. Assonova, V. D. Budaev, “The Hilbert and Bessel properties of systems of eigenfunctions of second-order operators”, Differ. Uravn., 36:2 (2000), 147–151; Differ. Equ., 36:2 (2000), 169–174
V. D. Budaev, “On Hilbert and Bessel inequalities for some sine, cosine and exponential systems”, Differ. Uravn., 33:1 (1997), 19–24; Differ. Equ., 33:1 (1997), 18–23
1996
6.
V. D. Budaev, “Some properties of root functions of differential operators that are connected with the unconditional basis property”, Differ. Uravn., 32:1 (1996), 9–14; Differ. Equ., 32:1 (1996), 8–14
1993
7.
V. D. Budaev, “Necessary conditions for the unconditional basis property of
systems of root functions of nonselfadjoint differential operators”, Dokl. Akad. Nauk, 329:4 (1993), 396–399; Dokl. Math., 47:2 (1993), 257–261
8.
V. D. Budaev, “Some properties of root vector functions of a higher-order operator”, Differ. Uravn., 29:1 (1993), 30–40; Differ. Equ., 29:1 (1993), 23–32
9.
V. D. Budaev, “A necessary condition for the Riesz basis property of systems of root functions of an ordinary nonselfadjoint differential operator”, Differ. Uravn., 29:1 (1993), 20–29; Differ. Equ., 29:1 (1993), 14–22
1992
10.
V. D. Budaev, “The unconditional basis property of systems of root vector
functions of differential operators with matrix coefficients”, Dokl. Akad. Nauk, 323:6 (1992), 999–1003; Dokl. Math., 45:2 (1992), 454–458
11.
V. D. Budaev, “Some properties of root functions of higher-order ordinary differential operators”, Differ. Uravn., 28:8 (1992), 1454–1456
12.
V. D. Budaev, “Criteria for the Bessel property and the Riesz basis property of systems of root functions of differential operators. II”, Differ. Uravn., 28:1 (1992), 23–33; Differ. Equ., 28:1 (1992), 21–30
1991
13.
V. D. Budaev, “A necessary condition for the Riesz basis property of systems of
root functions of ordinary differential operators”, Dokl. Akad. Nauk SSSR, 321:5 (1991), 873–875; Dokl. Math., 44:3 (1992), 797–799
14.
V. D. Budaev, “On the Bessel inequality for systems of root functions of
differential operators”, Dokl. Akad. Nauk SSSR, 318:1 (1991), 16–20; Dokl. Math., 43:3 (1991), 639–643
15.
V. D. Budaev, “Criteria for the Bessel property and the Riesz basis property of systems of root functions of differential operators. I”, Differ. Uravn., 27:12 (1991), 2033–2044; Differ. Equ., 27:12 (1991), 1421–1432
V. D. Budaev, “A condition for the unconditional basis property for systems of
eigen- and associated functions of ordinary differential operators”, Dokl. Akad. Nauk SSSR, 314:1 (1990), 25–28; Dokl. Math., 42:2 (1991), 252–255
1987
17.
V. D. Budaev, “The convergence of spectral expansions at the point of discontinuity of the coefficients of a linear nonselfadjoint differential operator of order $2m$”, Dokl. Akad. Nauk SSSR, 296:4 (1987), 780–784; Dokl. Math., 36:2 (1988), 309–313
18.
V. D. Budaev, “On the convergence of spectral expansions at the point of
discontinuity of the coefficients of a second-order linear nonselfadjoint
differential operator”, Dokl. Akad. Nauk SSSR, 293:2 (1987), 270–274
V. D. Budaev, “The property of being an unconditional basis on a closed interval, for systems of eigen- and associated functions of a second-order operator with discontinuous coefficients”, Differ. Uravn., 23:6 (1987), 941–952
V. D. Budaev, “An estimate for the modulus of the derivative of a regular solution of an ordinary linear differential equation”, Differ. Uravn., 23:2 (1987), 198–204
1986
21.
V. D. Budaev, “The property of being an unconditional basis of systems of eigen- and associated functions of a second-order operator with discontinuous coefficients”, Dokl. Akad. Nauk SSSR, 289:4 (1986), 777–780
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