Compactly supported wavelets preserving localization with the growth of smoothness are constructed. Asymptotics of zeros of Bernstein polynomials used in the above mentioned construction is investigated. Nonstationary orthonormal infinitily differentiable compactly supported wavelets are constructed.
Biography
Graduated from Faculty of Mathematics and Mechanics of Samara State University in 1980 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1984. D.Sci. thesis was defended in 2000. A list of my works contains more than 50 titles.
Main publications:
Novikov I., Semenov E. Haar series and linear operators. Dordrecht: Kluwer Acad. Publ., 1996. (Math. Appl., V.367.)
E. A. Kiselev, L. A. Minin, I. Ya. Novikov, S. N. Ushakov, “Localization of the window functions of dual and tight Gabor frames generated by the Gaussian function”, Sb. Math., 215:3 (2024), 364–382
2023
2.
M. L. Minina, E. A. Kiselev, I. Ya. Novikov, S. N. Ushakov, “Hermitian Interpolation Using Window Systems Generated by Uniform Shifts of the Gaussian Function”, Math. Notes, 114:6 (2023), 1502–1505
2020
3.
M. G. Zimina, S. I. Makarov, I. Ya. Novikov, “Asymptotics of the Roots of Bernstein Polynomials Used in the Construction of Modified Daubechies Wavelets”, Math. Notes, 107:5 (2020), 828–832
2019
4.
E. A. Kiselev, L. A. Minin, I. Ya. Novikov, “Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames”, Math. Notes, 106:1 (2019), 71–80
2016
5.
E. A. Kiselev, L. A. Minin, I. Ya. Novikov, “Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions”, Sb. Math., 207:8 (2016), 1127–1141
6.
L. A. Minin, I. Ya. Novikov, S. N. Ushakov, “On Expansion with Respect to Gabor Frames Generated by the Gaussian Function”, Math. Notes, 100:6 (2016), 890–892
2015
7.
"I. Ya. Novikov, S. Ya. Novikov ", “USTOIChIVOST IZMERITELNOGO OTOBRAZhENIYa”, SOVREMENNYE METODY TEORII FUNKTsII I SMEZhNYE PROBLEMY, Materialy Mezhdunarodnoi konferentsii, 2015, “87-89”
2014
8.
E. A. Kiselev, L. A. Minin, I. Ya. Novikov, S. M. Sitnik, “On the Riesz Constants for Systems of Integer Translates”, Math. Notes, 96:2 (2014), 228–238
9.
E. A. Kiselev, L. A. Minin, I. Ya. Novikov, “On the Construction of Biorthogonal Systems for Subspaces Generated by Integral Shifts of a Single Function”, Math. Notes, 96:3 (2014), 451–453
10.
M. V. Zhuravlev, I. Ya. Novikov, S. N. Ushakov, “On the uncertainty constants for linear combination of some subsystems of coherent states”, Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2014, no. 7(118), 17–31
2012
11.
I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898
2010
12.
I. Ya. Novikov , G. Yu. Severin, “NEPOSREDSTVENNYI SINTEZ SISTEMY ORTOGONALNYKh FINITNYKh FUNKTsII NA PRIMERE URAVNENIYa KORTEVEGA-DE-FRIZA”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika., 2010, no. 1 , 4 pp., S. 155-158. http://elibrary.ru/item.asp?id=15198852
I. Ya. Novikov, V. Yu. Protasov , M. A. Skopina, Teoriya Vspleskov, FIZMATLIT, 2005 , 612 pp. http://elibrary.ru/item.asp?id=24057250
2003
15.
I. Ya. Novikov, E. M. Semenov, “O PROBLEMAKh GEOMETRII BANAKhOVYKh PROSTRANSTV”, Veduschie nauchno-pedagogicheskie kollektivy, eds. A. S. Sidorkin, Voronezh, 2003, “17-24”. http://elibrary.ru/item.asp?id=21726640
2002
16.
I. Ya. Novikov, “Asymptotics of the Roots of Bernstein Polynomials Used in the Construction of Modified Daubechies Wavelets”, Math. Notes, 71:2 (2002), 217–229
2001
17.
I. Ya. Novikov, “Compactly supported wavelets”, Fundam. Prikl. Mat., 7:4 (2001), 955–981
18.
Novikov I.Ya., “SOOTNOShENIYa MEZhDU RADIUSAMI MASShTABIRUYuSchEGO FILTRA I MASShTABIRUYuSchEI FUNKTsII VSPLESKOV”, Trudy matematicheskogo fakulteta, eds. V. I. Ovchinnikov, Voronezhskii gosudarstvennyi unniversitet, Voronezh, 2001, 90-101 http://elibrary.ru/item.asp?id=23375501
2000
19.
S. K. Gorlov, I. Ya. Novikov, V. A. Rodin, “Correction of Haar polynomials used in the compression of graphical information”, Russian Math. (Iz. VUZ), 44:7 (2000), 4–8
20.
I. Ya. Novikov, “NESTATsIONARNYE BESKONEChNO DIFFERENTsIRUEMYE VSPLESKI S KOMPAKTNYMI NOSITELYaMI I RAVNOMERNO OGRANIChENNYMI KONSTANTAMI NEOPREDELENNOSTI”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika., 2000, no. 1 , 11 pp., S. 132-142. http://elibrary.ru/author_items.asp?authorid=4577
1998
21.
I. Ya. Novikov, S. B. Stechkin, “Basic wavelet theory”, Russian Math. Surveys, 53:6 (1998), 1159–1231
22.
I. Ya. Novikov, “UNCERTAINTY CONSTANTS FOR MODIFIED DAUBECHIES WAVELETS”, Izvestiya Tulskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Informatika, 4 (1998) , 5 pp., S. 107. http://elibrary.ru/author_items.asp?authorid=4577
1997
23.
I. Ya. Novikov, S. B. Stechkin, “Basic constructions of wavelets”, Fundam. Prikl. Mat., 3:4 (1997), 999–1028
1995
24.
M. Z. Berkolaiko, I. Ya. Novikov, “Bases of splashes and linear operators in anisotropic Lizorkin–Triebel spaces”, Proc. Steklov Inst. Math., 210 (1995), 2–21
25.
I. Ya. Novikov, M. Z. Berkolaiko, “BAZISY VSPLESKOV I LINEINYE OPERATORY V ANIZOTROPNYKh PROSTRANSTVAKh LIZORKINA -TRIBELYa.”, Doklady Akademii nauk., 340. (1995) , 1 pp., C.583
26.
M. Z. Berkolaiko, I. Ya. Novikov, “Wavelet bases and linear operators in anisotropic Lizorkin–Triebel spaces”, Dokl. Akad. Nauk, 340:5 (1995), 583–586
27.
E. M. Semenov, M. Z. Berkolaiko, I. Ya. Novikov, V. A. Rodin , A. A. Sedaev, “LINEINYE OPERATORY I BAZISY FUNKTsIONALNYKh PROSTRANSTV”, otchet o NIR # 95-01-00135 (Rossiiskii fond fundamentalnykh issledovanii), 1995 http://elibrary.ru/item.asp?id=222488
1994
28.
M. Z. Berkolaiko, I. Ya. Novikov, “On infinitely smooth compactly supported almost-wavelets”, Math. Notes, 56:3 (1994), 877–883
29.
M. Z. Berkolaiko, I. Ya. Novikov, “Images of wavelets under the influence of convolution operators”, Math. Notes, 55:5 (1994), 446–454
30.
I. Ya. Novikov, “ON THE CONSTRUCTION OF NONSTATIONARY ORTHONORMAL INFINITELY DIFFERENTIABLE COMPACTLY SUPPORTED WAVELETS”, Functional Differential Equations, 2. (1994) , 5 pp., S. 145.
1993
31.
I. Ya. Novikov, “Martingale inequalities in rearrangement invariant spaces”, Siberian Math. J., 34:1 (1993), 99–105
1994
32.
M. Z. Berkolaiko, I. Ya. Novikov, “Unconditional bases in spaces of functions of anisotropic smoothness”, Proc. Steklov Inst. Math., 204 (1994), 27–41
1992
33.
I. Ya. Novikov, “Wavelets of Y. Meyer – an optimal basis in $C(0,1)$”, Math. Notes, 52:5 (1992), 1137–1140
34.
I. Ya. Novikov, “Equivalent criterion of Haar and Franklin systems in symmetric spaces”, Math. Notes, 52:3 (1992), 943–947
35.
I. Ya. Novikov, M. Z. Berkolaiko, “BAZISY VSPLESKOV V PROSTRANSTVAKh DIFFERENTsIRUEMYKh FUNKTsII ANIZOTROPNOI GLADKOSTI”, Doklady Akademii nauk, T. 323 (1992) , 1 pp., S. 615.
36.
M. Berkolaiko, I. Ya. Novikov, “O BESKONEChNO GLADKIKh POChTI-VSPLESKAKh S KOMPAKTNYM NOSITELEM”, Doklady Akademii nauk, 326:6 (1992) , 1 pp., S. 935.
37.
M. Z. Berkolaiko , I. Ya. Novikov, “BASES OF WAVELETS IN SPACES OF DIFFERENTIABLE FUNCTIONS OF ANISOTROPIC SMOOTHNESS”, Doklady Mathematics, 45 (1992) , 1 pp., S. 382.
38.
M. Z. Berkolaiko, I. Ya. Novikov, “Wavelet bases in spaces of differentiable functions of anisotropic
smoothness”, Dokl. Math., 45:2 (1992), 382–386
1993
39.
M. Z. Berkolaiko, I. Ya. Novikov, “Infinitely smooth almost-wavelets with compact support”, Dokl. Math., 46:2 (1993), 378–382
1988
40.
I. Ya. Novikov, V. A. Rodin, “Characterization of points of $p$-strong summability of trigonometric series, $p\geq 2$”, Soviet Math. (Iz. VUZ), 32:9 (1988), 86–91
1984
41.
I. Ya. Novikov, E. M. Semenov, “Fourier-Haar coefficients”, Math. Notes, 36:3 (1984), 673–677
42.
I. Ya. Novikov, “On subsequences of the Haar system in $L_1$”, Russian Math. Surveys, 39:1 (1984), 175–176
43.
M. Sh. Braverman, I. Ya. Novikov, “Subspaces of symmetric spaces generated by independent random variables”, Siberian Math. J., 25:3 (1984), 361–370
1983
44.
I. Ya. Novikov, “SEQUENCES OF CHARACTERISTIC FUNCTIONS IN SYMMETRIC SPACES”, Sibirskii matematicheskii zhurnal, 24 (1983) , 5 pp., S. 193.
45.
I. Ya. Novikov, “Sequences of characteristic functions in symmetric spaces”, Sibirsk. Mat. Zh., 24:2 (1983), 193–196
2024
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