Analysis Mathematica

, Volume 19, Issue 1, pp 65–84 | Cite as

Thep-adic differential-integral type operator

  • He Zelin
Article
Received:

Keywords

Type Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

p-АДИЧЕскИИ ОпЕРАтОР ДИФФЕРЕНцИАльНО-ИНт ЕгРАльНОгО тИпА

Abstract

стАтьь пОсВьЩЕНА кРУ гУ ВОпРОсОВ, ОтНОсьЩИ хсь к ВЕсьМА ОБЩЕИ тЕОРИИp-АДИЧ Еск ОгО ИсЧИслЕНИь, ОсНОВыВА УЩЕИсь НА РАБОтАх гИБ БсА, БУтцЕРА, ВАгНЕРА, ОННЕВЕРА, шИп пА, пАлА И шИМОНА И ДРУгИх. АВтО Р ВВОДИт НЕкОтОРОЕ шИ РОкОЕ сЕМЕИстВО ОпЕРАтОРО В —p-АДИЧЕскИх ОпЕРАтОРОВ ДИФФЕРЕН цИАльНО-ИНтЕгРАльНО гО тИпА — И пОНьтИЕ пОРьДкОВОгО тИпА ОпЕРАтОРА, ЧтО ДАЕт УНИФИцИРОВА ННОЕ И ДАлЕкО ИДУЩЕЕ О БОБЩЕНИЕ пОНьтИИ пРОИжВОДНОИ И ИНтЕгРАлА БУтцЕРА И ВАгНЕРА.

ВВОДьтсь тАкжЕ сООтВ ЕтстВУУЩИЕ пОНьтИь Н АИлУЧшЕгО пРИБлИжЕНИь, МОДУль Н ЕпРЕРыВНОстИ, лИпшИцЕВых клАссОВ Ф УНкцИИ И т.л. Дль НИх УстАНАВлИВАУтсь ВЕс ьМА ОБЩИЕ тЕОРЕМы тИпА тЕОРЕМ ВАтАРИ, БЕ РНштЕИНА И ДжЕксОНА.

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. L. Butzer andH. J. Wagner, Walsh-Fourier series and the concept of derivative,Applicable Anal.,3 (1973), 29–46.Google Scholar
  2. [2]
    P. L.Butzer and H. J.Wagner, A calculus for Walsh functions defined onR +,Proc. Symp. On applications of Walsh functions, Washington, D. C., 1973, 75–81.Google Scholar
  3. [3]
    P. L. Butzer, W. Engels andU. Wipperfürth, An extension of the dyadic calculus with fractional order derivatives,Comp. and Maths. with Appls., Vol.1213, No. 5/6 (1986), 1073–1090.Google Scholar
  4. [4]
    J. E. Gibbs,Functions that are solutions of a logical differential equation, NPL, Middlesex, England, DES. rept. No.4 (1970).Google Scholar
  5. [5]
    He Zelin, Derivatives and integrals of fractional order in generalized Walsh-Fourier analysis, with applications to approximation theory,J. Approx. Theory,39 (1983), 216–273.Google Scholar
  6. [6]
    He Zelin, On representation of quasi-convex functions byL(R +)-Walsh transforms,J. of Nanjing University Math.,1 (1987) 16–20.Google Scholar
  7. [7]
    HeZelin and D.Mustard, Convergence properties of a class of Walsh-Fourier integral operators,Proc. Internat. Workshop on Gibbs derivatives, Kupari-Dobrovnik, 1989; 145–156.Google Scholar
  8. [8]
    He Zelin andD. Mustard, The type of a class of Walsh-Fourier convolution operators,Proc. Amer. Math. Soc.,116 (1992), 711–719.Google Scholar
  9. [9]
    C. W. Onneweer, Fractional differentiation on the group of integers ofp-adic or p-series field,Analysis Math.,3 (1977), 119–130.Google Scholar
  10. [10]
    J. Pál andP. Simon, On a generalization of the concept of derivative,Acta Math. Hungar.,29 (1976), 155–164.Google Scholar
  11. [11]
    F. Schipp, On term by term dyadic differentiability of Walsh series,Analysis Math.,2 (1976), 149–154.Google Scholar
  12. [12]
    R. C. Selfridge, Generalized Walsh transform,Pacific J. Math.,5 (1955), 451–480.Google Scholar
  13. [13]
    H. J.Wagner, On dyadic calculus for functions defined onR +,Proc. Symp. Theory and Applications of Walsh functions, Symp. Hatfield, Herts., July 1–3, 1975; 101–129.Google Scholar
  14. [14]
    C.Watari, Approximation of functions by a Walsh-Fourier series,Proc. Symp. on Applications of Walsh functions, Washington, D. C. 1970, 166–169.Google Scholar
  15. [15]
    Zheng Weixing andSu Weiyi, The logical derivative and integral,J. Math. Res. exposition,1 (1981), 79–90.Google Scholar

Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • He Zelin
    • 1
  1. 1.Department of MathematicsNanjing UniversityNanjingPeople's Republic of China

Personalised recommendations