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О Сходимости Тригонометричецкого и Гармонического интерполирования

О Сходимости Тригонометричецкого и Гармонического интерполирования 0 CXO~HMOCTI/I TPHFOHOMETPHqECKOFO H FAPMOHHqECKOFO I/IHTEP I1OflI/IPOBAH H~I O. KFIILI (By~anemO (FIpe~cTa~aeno A. P e u s n) B HaCTOnIi~efi pa6oTe npHBe/IeHbI Heo6xo~nMbm r~ ~OCTaTOqHbIe yC~OBri~t, KOTOpbIe Halo HaYlo)KHTb Ha Ma~rpnay ya.~OB, qTO6bI ~Me~a MeCTO TpnroHoMeTp~qec~oro HHTepnoanpoBam~ ~ He~oTopLIx ~aaccoB nepuo~n- qecKHx qbynKuHfi. XOT~ H3yqeHmO TpHrouoMeTp~qec~0ro HnTepnoanpoBamia nocs~mena o6nmpna~ aHTepaTypa, MHe n3BeCTeH JH4mb O~HH peay~bTaT TaKoro po~a. DTO Cq~OpMy~npOBaHnoe X. Xa H O M B pa6oTe [11] neo6x0~uMoe n ~OCTaTOqHOe ycaoB~e-CXO~Z~OCT~ ~ Vo~ax ~enpep~mHOCT~ ~ym(;infi c orpa~e~n~m ~aMeHeuneM o6mero nnTepnoa~R~onHoro npoRecca, qaCTHbIM cnyuaeM ~OTO- poro ~Ba~eTc~ TpHrOHO~ewpH~eci(oe HHTepnoa~pOBaH~e. ([lpaB~abHoe ~oKa3a- TeabCTBO ROCTaTOqHOCT~ aToro ycaoBu~ 6~IaO ~aHO C, M. 30 a~ a c ~M B CTaTbe [7].) Hn~e CqbopMy~mpoBaHHbt ~eo6x0R~bte ~ RocTaToqttbIe yCYIOBHgl paBuo~epHofi ~a ~cefi BeIKeCTBe~tr!O~ OC~ vp~roHor~ewp~qec~oro IdHTepn0r npo~tecca ~a~I MHO~eCTBa nepno~n~ec~x n ana~.T~ ~ec~nx Ha BemecTseHnofi ocri ~yH~aHfi (w 5, weopeMa 51), ~aa ~cex Hec~oab~o paa Henpep~mno ~O~qbepena~pyeM~ix nepno~ec~x dpyu~t~fi (w 7, ~eope~a 8), ~3t~ npocTpaHcw~a nepi~o~ec~Hx 0pyH~t~fi, n~e~otu~x Hec~o3b~o a6comoT~o Henpepu~s~x npoa3Bo~x (w Teope~a 7), ~ ~ scex nep~o~H~ecKHx ~yn~ttv, fi, n~ae~m~x nec~ooa~o npon~BO~l~x c orpaHrmenHH;a n~MeneH~e~,; (w 9, Teope~a 9). B noc3e~HnX TPeX cay~anx ~tan0 Ta~e Heo6xo~nMoe ~ ~ocTaTO~oe yCaoBne CXO~nMOCTH Tpnrouo~eTpn~ec~oro nHTepnoaHpoBannn B OT~ea~HSIX To~ax. lqpnBe~ena ~aK~e HanMeH~maa aa~HyTan o6aaCTb, o6aa~a- ~omaa Te~ cBoI4CTBOM, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

О Сходимости Тригонометричецкого и Гармонического интерполирования

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF02028203
Publisher site
See Article on Publisher Site

Abstract

0 CXO~HMOCTI/I TPHFOHOMETPHqECKOFO H FAPMOHHqECKOFO I/IHTEP I1OflI/IPOBAH H~I O. KFIILI (By~anemO (FIpe~cTa~aeno A. P e u s n) B HaCTOnIi~efi pa6oTe npHBe/IeHbI Heo6xo~nMbm r~ ~OCTaTOqHbIe yC~OBri~t, KOTOpbIe Halo HaYlo)KHTb Ha Ma~rpnay ya.~OB, qTO6bI ~Me~a MeCTO TpnroHoMeTp~qec~oro HHTepnoanpoBam~ ~ He~oTopLIx ~aaccoB nepuo~n- qecKHx qbynKuHfi. XOT~ H3yqeHmO TpHrouoMeTp~qec~0ro HnTepnoanpoBamia nocs~mena o6nmpna~ aHTepaTypa, MHe n3BeCTeH JH4mb O~HH peay~bTaT TaKoro po~a. DTO Cq~OpMy~npOBaHnoe X. Xa H O M B pa6oTe [11] neo6x0~uMoe n ~OCTaTOqHOe ycaoB~e-CXO~Z~OCT~ ~ Vo~ax ~enpep~mHOCT~ ~ym(;infi c orpa~e~n~m ~aMeHeuneM o6mero nnTepnoa~R~onHoro npoRecca, qaCTHbIM cnyuaeM ~OTO- poro ~Ba~eTc~ TpHrOHO~ewpH~eci(oe HHTepnoa~pOBaH~e. ([lpaB~abHoe ~oKa3a- TeabCTBO ROCTaTOqHOCT~ aToro ycaoBu~ 6~IaO ~aHO C, M. 30 a~ a c ~M B CTaTbe [7].) Hn~e CqbopMy~mpoBaHHbt ~eo6x0R~bte ~ RocTaToqttbIe yCYIOBHgl paBuo~epHofi ~a ~cefi BeIKeCTBe~tr!O~ OC~ vp~roHor~ewp~qec~oro IdHTepn0r npo~tecca ~a~I MHO~eCTBa nepno~n~ec~x n ana~.T~ ~ec~nx Ha BemecTseHnofi ocri ~yH~aHfi (w 5, weopeMa 51), ~aa ~cex Hec~oab~o paa Henpep~mno ~O~qbepena~pyeM~ix nepno~ec~x dpyu~t~fi (w 7, ~eope~a 8), ~3t~ npocTpaHcw~a nepi~o~ec~Hx 0pyH~t~fi, n~e~otu~x Hec~o3b~o a6comoT~o Henpepu~s~x npoa3Bo~x (w Teope~a 7), ~ ~ scex nep~o~H~ecKHx ~yn~ttv, fi, n~ae~m~x nec~ooa~o npon~BO~l~x c orpaHrmenHH;a n~MeneH~e~,; (w 9, Teope~a 9). B noc3e~HnX TPeX cay~anx ~tan0 Ta~e Heo6xo~nMoe ~ ~ocTaTO~oe yCaoBne CXO~nMOCTH Tpnrouo~eTpn~ec~oro nHTepnoaHpoBannn B OT~ea~HSIX To~ax. lqpnBe~ena ~aK~e HanMeH~maa aa~HyTan o6aaCTb, o6aa~a- ~omaa Te~ cBoI4CTBOM,

Journal

Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: Jul 16, 2005

References

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    Kalmár, L.
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    Киш, О.
  • Об опредении наименьшей области, голоморфность в которой обеспечивает сходимость эрмитовского интерпированиь при любой системе узлов
    Крылов, В. И.
  • О сходимости алгебраического интерполирования в классах дифференцруемых функциь
    Крылов, В. И.
  • Über das Interpolationsproblem
    Hahn, H.