Akcije

Mathematica Moravica
kako citirati ovaj članak
podeli ovaj članak
Direktan link

Metrika

  • citati u SCIndeksu: [3]
  • citati u CrossRef-u:[7]
  • citati u Google Scholaru:[]
  • posete u poslednjih 30 dana:3
  • preuzimanja u poslednjih 30 dana:1

Sadržaj

članak: 1 od 1  
Mathematica Moravica
2003, br. 7, str. 107-152
Fundamental facts on translational O-regularly varying functions
(naslov ne postoji na srpskom)
Tasković Milan R.
Univerzitet u Beogradu, Matematički fakultet, Srbija
Sažetak
(ne postoji na srpskom)
In this paper we introduce three new classes of functions under names translational slowly varying, translational regularly varying and translational O-regularly varying functions. All classes have important applications in the study of asymptotic processes. In this sense, Uniform Convergence Theorem, Characterization Theorem and Representation Theorem are the main results of this paper for all cite classes of functions. This results are closely connected with the Karamata's theory of regularly varying functions. Also, in this paper we introduce three classes of sequences under names translational slowly varying, translational regularly varying and translational O-regularly varying sequences. All three classes have important applications in the study of asymptotic processes. The results are of relevance in connection with limit statements in various branches of probability theory and ergodic theory.
Reference

Aczel, J. (1966) Functional equations and their applications. New York-San Diego, itd: Academic Press

1

Aljančić, S., Aranđelović, D. (1977) O-regularly varying functions. Publications de l'Institut mathematique, 22(36), 5-22

1

Ash, J.M., Erdös, P., Rubel, L.A. (1974) Very slowly varying functions. Aequationes Mathematicae / AEM, 10, 1-9

Avakumović, V.G. (1936) On a O-inverse theorem. Zagreb: Jugoslavenska akademija znanosti i umjetnosti / JAZU, (in Serbian), t. 254, Razreda Matematičko-Prirodoslovnoga 79) 167-186

Bari, N.K., Stechkin, S.B. (1956) Best approximations and differential properties of two conjugate functions. Trudy Moskov. Mat. Obsc., 5, 483-522

Baummann, H. (1967) Umkehrsätze für das asymptotische Verhalten linearer Folgentransformationen. Mathematische Zeitschrift, 98, 140-178

15

Bingham, N.H., Goldie, C.M., Teugels, J.L. (1987) Regular variation. u: Encyclopedia of Mathematics and its Applications, Cambridge, itd: Cambridge University Press / CUP

Bojanić, R., Karamata, J. (1963) On slowly varying functions and asymptotic relations. Madison, WI: University of Wisconsin - Math. Res. Centre Tech, Summary Report 432

1

Bojanić, R., Seneta, E. (1971) Slowly varying functions and asymptotic relations. Journal of Mathematical Analysis and Applications, 34, 302-315

2

Bojanić, R., Seneta, E. (1973) A unified theory of regularly varying sequences. Mathematische Zeitschrift, 134, 91-106

1

de Bruijn, N.G. (1959) Pairs of slowly oscillating functions occurring in asymptotic problems concerning the Laplace transform. Nieuw Arch. Wisk, 7, 20-26

3

de Haan, L. (1970) On regular variation and its applications to the weak convergence of sample extrems. u: Mathematical Centre Tracts, Amsterdam, 32

Delange, H. (1955) Sur un th\'eor\'eme de Karamata. Bulletin des Sciences Mathematiques, 79, 9-12

Đurčić, D. (1998) $\scr O$-regularly varying functions and strong asymptotic equivalence. Journal of Mathematical Analysis and Applications, 220, 2, 451-461

1

Galambos, J., Seneta, E. (1973) Regularly varying sequences. Proc. Amer. Math. Soc., 41, 110-116

1

Hardy, G.H., Littlewood, J.E. (1929) Notes on the theory of series XI-On Tauberian theorems. Proceedings of the London Mathematical Society, 30, 23-37

1

Karamata, J. (1930) Sur certains Tauberian theorems de M. M. Hardy et Littlewood. Mathematica, Cluj, 3, 33-48

6

Karamata, J. (1930) Sur un mode de croissance reguliere des fonctions. Mathematica, Cluj, 4, 38-53

1

Karamata, J. (1933) Sur un mode de croissance r\'eguli\'ere. Th\'eor\'emes fondamentaux. Bull. Soc. Math. France, 61, 55-62

1

Karamata, J. (1936) Bemerkung über die vorstehende Arbeit des Herrn Avakumović mit näherer Betrachtung einer Klasse von Funktionen, welche bei den Inversionssätzen vorkommen. Bull. International, de l'Academie Yougoslave, Zagreb, 29 et 30, 117-123

Kingman, J.F.C. (1963) Ergodic properties of continuous-time Markov processes and their discrete skeletons. Proceedings of the London Mathematical Society, 13, 593-604

Lamperti, J. (1967) Limiting distributions for branching processes. u: le Cam L., Neyman J. [ur.] Proc. 5th Berkeley Symp. on Math. Stat. and Prob, Berkeley, CA, itd: University of California Press, vol. II, Part 2 str. 225-241

1

Matuszewska, W. (1962) Regularly increasing functions in connection with the theory of $L\sp{*\phi }$-spaces. Studia Mathematica, 21, 317-344

1

Matuszewska, W., Orlicz, W. (1965) On some classes of functions with regard to their orders of growth. Studia Mathematica, 26, 11-24

Polya, G. (1923) Bemerkungen über unendliche Folgen und ganze Funktionen. Mathematische Annalen, 88, 169-183

3

Schmidt, R. (1925) Uber divergente Folgen und lineare Mittelbildungen. Mathematische Zeitschrift, 22, 1, 89-152

1

Schur, I. (1930) Zur Theorie der Cesaroschen und Hölderschen Mittelwerte. Mathematische Zeitschrift, 31, 1, 391-407

8

Seneta, E. (1976) Regularly varying functions. Lecture Notes in Mathematics, 508, 112

Slack, R.S. (1973) Further notes on branching processes with mean 1. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 25, 31-38

Tasković, M.R. (2001) Translational regularly varying functions. to appear

Tasković, M.R. (2001) Translational O-regularly varying functions. to appear

1

van Aardenne-Ehrenfest, T., de Bruijn, N.G., Korevaar, J. (1949) A note on slowly oscillating functions. Nieuw Arch. Wisk, 23, 77-86

Vuilleumier, M. (1967) Sur le comportement asymptotique des transformations lin\'eaires des suites. Mathematische Zeitschrift, 98, 126-139

12

Zygmund, A. (1968) Trigonometric series. Cambridge, itd: Cambridge University Press / CUP, vol. 1
   

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor0307107T
objavljen u SCIndeksu: 02.06.2007.

Povezani članci

Nema povezanih članaka