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.)
I. Ya. Novikov, S. B. Stechkin, “Basic wavelet theory”, Russian Math. Surveys, 53:6 (1998), 1159–1231
2.
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
3.
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
4.
I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898
5.
I. Ya. Novikov, S. B. Stechkin, “Basic constructions of wavelets”, Fundam. Prikl. Mat., 3:4 (1997), 999–1028
6.
M. Z. Berkolaiko, I. Ya. Novikov, “On infinitely smooth compactly supported almost-wavelets”, Math. Notes, 56:3 (1994), 877–883
7.
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
8.
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
9.
I. Ya. Novikov, “Martingale inequalities in rearrangement invariant spaces”, Siberian Math. J., 34:1 (1993), 99–105
10.
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
11.
M. Z. Berkolaiko, I. Ya. Novikov, “Images of wavelets under the influence of convolution operators”, Math. Notes, 55:5 (1994), 446–454
12.
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
13.
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
14.
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
15.
M. Z. Berkolaiko, I. Ya. Novikov, “Unconditional bases in spaces of functions of anisotropic smoothness”, Proc. Steklov Inst. Math., 204 (1994), 27–41
16.
I. Ya. Novikov, “Wavelets of Y. Meyer – an optimal basis in $C(0,1)$”, Math. Notes, 52:5 (1992), 1137–1140
17.
M. Z. Berkolaiko, I. Ya. Novikov, “Wavelet bases in spaces of differentiable functions of anisotropic
smoothness”, Dokl. Math., 45:2 (1992), 382–386
18.
M. Z. Berkolaiko, I. Ya. Novikov, “Infinitely smooth almost-wavelets with compact support”, Dokl. Math., 46:2 (1993), 378–382
19.
M. Sh. Braverman, I. Ya. Novikov, “Subspaces of symmetric spaces generated by independent random variables”, Siberian Math. J., 25:3 (1984), 361–370
20.
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
21.
I. Ya. Novikov, “Equivalent criterion of Haar and Franklin systems in symmetric spaces”, Math. Notes, 52:3 (1992), 943–947
22.
I. Ya. Novikov, “Sequences of characteristic functions in symmetric spaces”, Sibirsk. Mat. Zh., 24:2 (1983), 193–196
23.
"I. Ya. Novikov, S. Ya. Novikov ", “USTOIChIVOST IZMERITELNOGO OTOBRAZhENIYa”, SOVREMENNYE METODY TEORII FUNKTsII I SMEZhNYE PROBLEMY, Materialy Mezhdunarodnoi konferentsii, 2015, “87-89”
24.
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, 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
28.
I. Ya. Novikov, “Compactly supported wavelets”, Fundam. Prikl. Mat., 7:4 (2001), 955–981
29.
Novikov I.Ya., “SOOTNOShENIYa MEZhDU RADIUSAMI MASShTABIRUYuSchEGO FILTRA I MASShTABIRUYuSchEI FUNKTsII VSPLESKOV”, Trudy matematicheskogo fakulteta, eds. V. I. Ovchinnikov, Voronezhskii gosudarstvennyi unniversitet, Voronezh, 2001, 90-101http://elibrary.ru/item.asp?id=23375501
30.
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
31.
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
32.
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
33.
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
34.
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
35.
I. Ya. Novikov, “ON THE CONSTRUCTION OF NONSTATIONARY ORTHONORMAL INFINITELY DIFFERENTIABLE COMPACTLY SUPPORTED WAVELETS”, Functional Differential Equations, 2. (1994) , 5 pp., S. 145.
36.
I. Ya. Novikov, M. Z. Berkolaiko, “BAZISY VSPLESKOV V PROSTRANSTVAKh DIFFERENTsIRUEMYKh FUNKTsII ANIZOTROPNOI GLADKOSTI”, Doklady Akademii nauk, T. 323 (1992) , 1 pp., S. 615.
37.
M. Berkolaiko, I. Ya. Novikov, “O BESKONEChNO GLADKIKh POChTI-VSPLESKAKh S KOMPAKTNYM NOSITELEM”, Doklady Akademii nauk, 326:6 (1992) , 1 pp., S. 935.
38.
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.
39.
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
40.
I. Ya. Novikov, E. M. Semenov, “Fourier-Haar coefficients”, Math. Notes, 36:3 (1984), 673–677
41.
I. Ya. Novikov, “On subsequences of the Haar system in $L_1$”, Russian Math. Surveys, 39:1 (1984), 175–176
42.
I. Ya. Novikov, “SEQUENCES OF CHARACTERISTIC FUNCTIONS IN SYMMETRIC SPACES”, Sibirskii matematicheskii zhurnal, 24 (1983) , 5 pp., S. 193.
43.
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
44.
M. Z. Berkolaiko, I. Ya. Novikov, “Wavelet bases and linear operators in anisotropic Lizorkin–Triebel spaces”, Dokl. Akad. Nauk, 340:5 (1995), 583–586
45.
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
