RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1998, Volume 53, Issue 6(324), Pages 53–128 (Mi umn89)  

This article is cited in 48 scientific papers (total in 48 papers)

Basic wavelet theory

I. Ya. Novikova, S. B. Stechkinb

a Voronezh State University
b Steklov Mathematical Institute, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm89

Full text: PDF file (893 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1998, 53:6, 1159–1231

Bibliographic databases:

UDC: 517.5
MSC: 42C40, 28C10, 41A17, 46E35, 47G30, 26B35
Received: 28.07.1998

Citation: I. Ya. Novikov, S. B. Stechkin, “Basic wavelet theory”, Uspekhi Mat. Nauk, 53:6(324) (1998), 53–128; Russian Math. Surveys, 53:6 (1998), 1159–1231

Citation in format AMSBIB
\Bibitem{NovSte98}
\by I.~Ya.~Novikov, S.~B.~Stechkin
\paper Basic wavelet theory
\jour Uspekhi Mat. Nauk
\yr 1998
\vol 53
\issue 6(324)
\pages 53--128
\mathnet{http://mi.mathnet.ru/umn89}
\crossref{https://doi.org/10.4213/rm89}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702694}
\zmath{https://zbmath.org/?q=an:0955.42019}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1998RuMaS..53.1159N}
\transl
\jour Russian Math. Surveys
\yr 1998
\vol 53
\issue 6
\pages 1159--1231
\crossref{https://doi.org/10.1070/rm1998v053n06ABEH000089}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000081776300002}


Linking options:
  • http://mi.mathnet.ru/eng/umn89
  • https://doi.org/10.4213/rm89
  • http://mi.mathnet.ru/eng/umn/v53/i6/p53

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Phys. Usp., 45:1 (2002), 27–57  mathnet  crossref  crossref  isi  elib
    2. Demjanovich, YK, “Wavelet decompositions in spline spaces on nonuniform meshes”, Doklady Mathematics, 65:1 (2002), 47  isi  elib
    3. A. B. Pevnyi, “Kratnomasshtabnyi analiz v prostranstve $\ell^2(\mathbb Z)$ na osnove diskretnykh splainov”, Sib. zhurn. vychisl. matem., 7:3 (2004), 261–275  mathnet  zmath
    4. P. S. Zykov, E. B. Postnikov, “The application of the wavelet transform with a piecewise linear basis to the evaluation of the Hankel transform”, Comput. Math. Math. Phys., 44:3 (2004), 396–400  mathnet  mathscinet  zmath  elib
    5. V. V. Yurinsky, J. M. Reis Gama, “On Distribution of Error of Linear Wavelet Estimator of Probability Density”, Lith Math J, 45:2 (2005), 152  crossref  mathscinet  elib  scopus  scopus
    6. Yu. K. Dem'yanovich, “Embedded Spaces of Trigonometric Splines and Their Wavelet Expansion”, Math. Notes, 78:5 (2005), 615–630  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Konenkov, AN, “The Cauchy problem for the heat equation in Zygmund spaces”, Differential Equations, 41:6 (2005), 860  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Dem'yanovich, YK, “Smoothness of spline spaces and wavelet decompositions”, Doklady Mathematics, 71:2 (2005), 220  zmath  isi  elib
    9. I. I. Kosenko, “Topological degree and approximation of solutions for nonregular problems of mechanics: Oscillations of satellites on elliptic orbits”, Journal of Mathematical Sciences, 149:5 (2008), 1539–1566  mathnet  crossref  mathscinet
    10. J. Gama, V. V. Yurinskii, “An exponential estimate for a wavelet density estimator”, Theory Probab. Appl., 51:4 (2007), 595–608  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Yu. K. Dem'yanovich, “Local wavelet basis for an irregular grid”, J. Math. Sci. (N. Y.), 141:6 (2007), 1618–1632  mathnet  crossref  mathscinet  zmath  elib  elib
    12. Golovinski, PA, “Scattering of ultrashort laser pulse by atomic systems”, Laser Physics Letters, 3:5 (2006), 259  crossref  adsnasa  isi  elib  scopus  scopus
    13. Golovinski P.A., Mihaylov E.M., “Linear scattering of ultrashort laser pulse by atom - art. no. 625609”, ICONO 2005: Ultrafast Phenomena and Physics of Superintense Laser Fields; Quantum and Atom Optics; Engineering of Quantum Information, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 6256, 2006, 25609–25609  isi
    14. R. R. Nigmatullin, “Nanoshumy: novye neinvazivnye metody kolichestvennogo «prochteniya» sluchainykh posledovatelnostei”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 149, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2007, 71–82  mathnet
    15. Yu. K. Dem’yanovich, “Minimal splines and wavelets”, Vestnik St Petersb Univ Math, 41:2 (2008), 88  crossref  mathscinet  zmath  scopus  scopus
    16. E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Wavelet method for solving the unsteady porous-medium flow problem with discontinuous coefficients”, Comput. Math. Math. Phys., 48:12 (2008), 2194–2210  mathnet  crossref  mathscinet  isi  elib
    17. Konenkov, AN, “Solutions of model heat problems in Zygmund spaces”, Differential Equations, 44:10 (2008), 1448  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. Du, XM, “A note of wavelet variance”, Communications in Statistics-Theory and Methods, 37:5 (2008), 737  crossref  mathscinet  isi  scopus  scopus
    19. E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations”, Comput. Math. Math. Phys., 48:2 (2008), 251–268  mathnet  crossref  mathscinet  zmath  isi  elib
    20. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    21. A. Yu. Trynin, “A generalization of the Whittaker-Kotel'nikov-Shannon sampling theorem for continuous functions on a closed interval”, Sb. Math., 200:11 (2009), 1633–1679  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part”, Comput. Math. Math. Phys., 49:9 (2009), 1554–1566  mathnet  crossref  zmath  isi  elib
    23. Makarov A.A., “Odin variant splain-veivletnogo razlozheniya prostranstv B-splainov”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2009, no. 2, 59–71  elib
    24. Esaulenko I.E., Serezhenko N.P., Semenov S.N., “Raspoznavanie patologicheskikh patternov elektroentsefalogramm s ispolzovaniem veivlet-analiza”, Sistemnyi analiz i upravlenie v biomeditsinskikh sistemakh, 8:4 (2009), 855–857  elib
    25. A. Yu. Trynin, “The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm–Liouville problem”, Russian Math. (Iz. VUZ), 54:11 (2010), 66–76  mathnet  crossref  mathscinet  elib
    26. A. Yu. Trynin, “On divergence of sinc-approximations everywhere on $(0,\pi)$”, St. Petersburg Math. J., 22:4 (2011), 683–701  mathnet  crossref  mathscinet  zmath  isi
    27. Abdolaziz Abdollahi, Jahangir Cheshmavar, Mohsen Taghavi, “Wavelets generated by the Rudin-Shapiro polynomials”, centr eur j math, 2010  crossref  mathscinet  isi  scopus
    28. E. A. Pleshcheva, “New generalization of orthogonal wavelet bases”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S124–S132  mathnet  crossref  isi  elib
    29. Dobrosotskaya J.A., Bertozzi A.L., “Wavelet analogue of the Ginzburg-Landau energy and its Gamma-convergence”, Interfaces Free Bound, 12:4 (2010), 497–525  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    30. Yu. K. Dem'yanovich, “Nonsmooth spline-wavelet decompositions and their properties”, J. Math. Sci. (N. Y.), 182:6 (2012), 761–778  mathnet  crossref  mathscinet
    31. Yu. K. Dem’yanovich, I. D. Miroshnichenko, “Nonsmooth spline-wavelet decompositions on a segment”, J Math Sci, 2012  crossref  mathscinet  scopus
    32. Sofiya Ostrovska, Ahmet Yaşar Özban, “On the Sets of Convergence for Sequences of the �-Bernstein Polynomials with �>1”, Abstract and Applied Analysis, 2012 (2012), 1  crossref  mathscinet  zmath  isi  scopus  scopus
    33. Akimov P.A., Mozgaleva M.L., “Nekotorye elementy kratnomasshtabnogo veivlet-analiza chast 1. ponyatie o veivletakh i kratnomasshtabnom veivlet-analize”, Vestnik MGSU, 2012, no. 7, 44–50  elib
    34. Akimov P.A., Mozgaleva M.L., “Nekotorye elementy kratnomasshtabnogo veivlet-analiza. chast 2. analiz i sintez”, Vestnik MGSU, 2012, no. 8, 60–65  elib
    35. V. P. Krivokolesko, E. K. Leinartas, “O tozhdestvakh s polinomialnymi koeffitsientami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:3 (2012), 56–62  mathnet
    36. B.A. Suleimanov, O.A. Dyshin, “Application of discrete wavelet transform to the solution of boundary value problems for quasi-linear parabolic equations”, Applied Mathematics and Computation, 219:12 (2013), 7036  crossref  mathscinet  zmath  isi  scopus  scopus
    37. J. A. Dobrosotskaya, A. L. Bertozzi, “Analysis of the Wavelet Ginzburg–Landau Energy in Image Applications with Edges”, SIAM J. Imaging Sci, 6:1 (2013), 698  crossref  mathscinet  zmath  isi  scopus  scopus
    38. A. Yu. Trynin, “On necessary and sufficient conditions for convergence of sinc-approximations”, St. Petersburg Math. J., 27:5 (2016), 825–840  mathnet  crossref  mathscinet  isi  elib
    39. A. Yu. Trynin, “On some properties of sinc approximations of continuous functions on the interval”, Ufa Math. J., 7:4 (2015), 111–126  mathnet  crossref  isi  elib
    40. A. Yu. Trynin, “Approximation of continuous on a segment functions with the help of linear combinations of sincs”, Russian Math. (Iz. VUZ), 60:3 (2016), 63–71  mathnet  crossref  isi
    41. A. Yu. Trynin, “Neobkhodimye i dostatochnye usloviya ravnomernoi na otrezke sink-approksimatsii funktsii ogranichennoi variatsii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:3 (2016), 288–298  mathnet  crossref  mathscinet  elib
    42. Dyshin O.A., “Wavelet Solving Method of Nonstasionary Liquid Filtration Problem in Crack-Porosity of Circular Form”, SOCAR Proc., 2016, no. 1, 67–79  crossref  isi  scopus  scopus
    43. Ushakova E.P., Ushakova K.E., “Localisation Property of Battle-Lemarie Wavelets' Sums”, J. Math. Anal. Appl., 461:1 (2018), 176–197  crossref  mathscinet  zmath  isi  scopus  scopus
    44. A. Yu. Trynin, “Uniform convergence of Lagrange–Sturm–Liouville processes on one functional class”, Ufa Math. J., 10:2 (2018), 93–108  mathnet  crossref  isi
    45. A. Yu. Trynin, “A criterion of convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of variation”, Russian Math. (Iz. VUZ), 62:8 (2018), 51–63  mathnet  crossref  isi
    46. Nasyrova M.G., Ushakova E.P., “Wavelet Bases and Entropy Numbers of Hardy Operator”, Anal. Math., 44:4 (2018), 543–576  crossref  mathscinet  zmath  isi  scopus
    47. A. Yu. Trynin, “Skhodimost protsessov Lagranzha–Shturma–Liuvillya dlya nepreryvnykh funktsii ogranichennoi variatsii”, Vladikavk. matem. zhurn., 20:4 (2018), 76–91  mathnet  crossref
    48. A. Yu. Trynin, “Sufficient condition for convergence of Lagrange–Sturm–Liouville processes in terms of one-sided modulus of continuity”, Comput. Math. Math. Phys., 58:11 (2018), 1716–1727  mathnet  crossref  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1377
    Full text:653
    References:68
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019