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Journal articles on the topic 'L^p convergence'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Krasniqi, Xhevat Z., Péter Kórus, and Ferenc Móricz. "Necessary conditions for the $L^{p}$-convergence $(0." Mathematica Bohemica 139, no. 1 (2014): 75–88. http://dx.doi.org/10.21136/mb.2014.143637.

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2

Barcelo, Juan A., and Antonio Corboda. "Band-Limited Functions: L p -Convergence." Transactions of the American Mathematical Society 313, no. 2 (June 1989): 655. http://dx.doi.org/10.2307/2001422.

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3

Barceló, Juan Antonio, and Antonio Juan Córdoba. "Band-limited functions: $L^p $-convergence." Bulletin of the American Mathematical Society 18, no. 2 (April 1, 1988): 163–67. http://dx.doi.org/10.1090/s0273-0979-1988-15635-2.

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4

Lassalle, Silvia, and Jos� G. Llavona. "Weak-Polynomial Convergence on Spaces ? p and L p." Positivity 8, no. 3 (September 2004): 283–96. http://dx.doi.org/10.1007/s11117-004-5008-x.

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5

Orhan, C., and İ. Sakaoğlu. "Rate of convergence in $$L_{p}$$ L p approximation." Periodica Mathematica Hungarica 68, no. 2 (May 20, 2014): 176–84. http://dx.doi.org/10.1007/s10998-014-0028-1.

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6

Barcel{ó, Juan A., and Antonio C{órdoba. "Band-limited functions: $L\sp p$-convergence." Transactions of the American Mathematical Society 313, no. 2 (February 1, 1989): 655. http://dx.doi.org/10.1090/s0002-9947-1989-0951885-1.

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7

Teel, A. R. "Asymptotic convergence from L/sub p/ stability." IEEE Transactions on Automatic Control 44, no. 11 (1999): 2169–70. http://dx.doi.org/10.1109/9.802938.

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8

QIU, Dehua, Pingyan CHEN, and Volodin ANDREI. "Complete moment convergence for L p -mixingales." Acta Mathematica Scientia 37, no. 5 (September 2017): 1319–30. http://dx.doi.org/10.1016/s0252-9602(17)30075-9.

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9

McIntosh, J. Strasser, and Bruce M. Bennett. "$L^P$ metric criteria for directed convergence." Communications in Information and Systems 2, no. 2 (2002): 167–82. http://dx.doi.org/10.4310/cis.2002.v2.n2.a4.

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10

Haščák, Alexander. "A strong convergence in $L^p$ and upper $q$-continuous operators." Czechoslovak Mathematical Journal 38, no. 3 (1988): 420–24. http://dx.doi.org/10.21136/cmj.1988.102237.

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11

Rzezuchowski, Tadeusz. "Strong convergence of selections implied by weak." Bulletin of the Australian Mathematical Society 39, no. 2 (April 1989): 201–14. http://dx.doi.org/10.1017/s0004972700002677.

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In some situations weak convergence in L1, implies strong convergence. Let P, L: T → C∘(ℝd) be measurable multifunctions (C∘(ℝd) being the set of closed, convex subsets of ℝd) the values L(t) affine sets and W(t) = P(t) ∩ L(t) extremal faces of P(t). Let pk be integrable selections of P, the projection of pk,(t) on L(t) and pk(t) on W(t). We prove that if converges weakly to zero then pk − k converges to zero in measure. We give also some extensions of this theorem. As applications to differential inclusions we investigate convergence of derivatives of convergent sequences of solutions and we describe solutions which are in some sense isolated. Finally we discuss what can be said about control functions u when the corresponding trajectories of ẋ = f(t, x, u) are convergent to some trajectory.

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12

Ivanov, K. G., and E. B. Saff. "Nongeometric Convergence of Best L p (p � 2) Polynomial Approximants." Proceedings of the American Mathematical Society 110, no. 2 (October 1990): 377. http://dx.doi.org/10.2307/2048080.

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13

Campiti, Michele, and Giorgio Metafune. "$L^p$-convergence of Bernstein-Kantorovich-type operators." Annales Polonici Mathematici 63, no. 3 (1996): 273–80. http://dx.doi.org/10.4064/ap-63-3-273-280.

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14

Zhengchang, Wu. "Convergence of subdivision schemes in L p spaces." Applied Mathematics-A Journal of Chinese Universities 16, no. 2 (June 2001): 171–77. http://dx.doi.org/10.1007/s11766-001-0024-0.

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15

Borgs, Christian, Jennifer T. Chayes, Henry Cohn, and Yufei Zhao. "An $L^{p}$ theory of sparse graph convergence II: LD convergence, quotients and right convergence." Annals of Probability 46, no. 1 (January 2018): 337–96. http://dx.doi.org/10.1214/17-aop1187.

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16

Kaya, Y. "A Weakly Convergence Result on p( x) L Spaces." Mathematical and Computational Applications 20, no. 2 (August 2015): 106–10. http://dx.doi.org/10.19029/mca-2015-009.

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17

Min, Guohua. "On Weighted L p -Convergence of Certain Lagrange Interpolation." Proceedings of the American Mathematical Society 116, no. 4 (December 1992): 1081. http://dx.doi.org/10.2307/2159492.

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18

Laurita, C., and G. Mastroianni. "L p -convergence of Lagrange interpolation on the semiaxis." Acta Mathematica Hungarica 120, no. 3 (June 4, 2008): 249–73. http://dx.doi.org/10.1007/s10474-008-7119-5.

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19

Ivanov, K. G., and E. B. Saff. "Nongeometric convergence of best $L\sb p\ (p\neq 2)$ polynomial approximants." Proceedings of the American Mathematical Society 110, no. 2 (February 1, 1990): 377. http://dx.doi.org/10.1090/s0002-9939-1990-1019751-7.

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20

ZHANG, KEWEI. "ON THE PRINCIPLE OF CONTROLLED L∞ CONVERGENCE IMPLIES ALMOST EVERYWHERE CONVERGENCE FOR GRADIENTS." Communications in Contemporary Mathematics 09, no. 01 (February 2007): 21–30. http://dx.doi.org/10.1142/s0219199707002320.

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Let Ω ⊂ ℝn be a bounded open set. If a sequence fk : Ω → ℝN converges to f in L∞ in a certain "controlled" manner while bounded in W1,p (1 < p < + ∞) or BV, we show that f ∈ W1,p (respectively, f ∈ BV) and ∇fk → ∇f almost everywhere, where ∇fk and ∇f are the usual gradients if fk ∈ W1,p (respectively, the absolutely continuous part of the gradient measures if fk ∈ BV). Our main theorem generalizes results for Lipschitz mappings. We show by an example that when p = 1, the limit of a sequence of increasing functions may fail to be in W1,1 and can even be nowhere C1.

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21

Kaur, Kulwinder, S. S. Bhatia, and Babu Ram. "Double trigonometric series with coefficients of bounded variation of higher order." Tamkang Journal of Mathematics 35, no. 3 (September 30, 2004): 267–80. http://dx.doi.org/10.5556/j.tkjm.35.2004.208.

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In this paper the following convergence properties are established for the rectangular partial sums of the double trigonometric series, whose coefficients form a null sequence of bounded variation of order $ (p,0) $, $ (0,p) $ and $ (p,p) $, for some $ p\ge 1$: (a) pointwise convergence; (b) uniform convergence; (c) $ L^r $-integrability and $ L^r $-metric convergence for $ 0

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22

Volosivets, S. S. "On Convergence of Fourier – Vilenkin Series in L p [0, 1), 0 < p ≤ 1." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 8, no. 3 (2008): 3–9. http://dx.doi.org/10.18500/1816-9791-2008-8-3-3-9.

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23

Qamaruddin, Q., and S. A. Mohiuddine. "Almost convergence and some matrix transformations." Filomat 21, no. 2 (2007): 261–66. http://dx.doi.org/10.2298/fil0702261q.

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24

Amirkhanyan, G. "Convergence of greedy algorithm in Walsh system in L p." Journal of Contemporary Mathematical Analysis 43, no. 3 (June 2008): 127–34. http://dx.doi.org/10.3103/s1068362308030011.

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25

Rybkin, A. V. "Convergence of Arguments of Blaschke Products in L p -Metrics." Proceedings of the American Mathematical Society 111, no. 3 (March 1991): 701. http://dx.doi.org/10.2307/2048407.

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26

Min, Guo Hua. "On weighted $L\sp p$-convergence of certain Lagrange interpolation." Proceedings of the American Mathematical Society 116, no. 4 (April 1, 1992): 1081. http://dx.doi.org/10.1090/s0002-9939-1992-1101990-x.

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27

Cattiaux, Patrick, Arnaud Guillin, and Cyril Roberto. "Poincaré inequality and the $L^p$ convergence of semi-groups." Electronic Communications in Probability 15 (2010): 270–80. http://dx.doi.org/10.1214/ecp.v15-1559.

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28

V�rtesi, P., and Y. Xu. "Weighted L p convergence of hermite interpolation of higher order." Acta Mathematica Hungarica 59, no. 3-4 (1992): 423–38. http://dx.doi.org/10.1007/bf00050905.

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29

Taggart, Robert J. "Pointwise convergence for semigroups in vector-valued L p spaces." Mathematische Zeitschrift 261, no. 4 (April 29, 2008): 933–49. http://dx.doi.org/10.1007/s00209-008-0360-3.

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30

Li, Lingqiang. "p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces." Mathematics 7, no. 3 (March 1, 2019): 228. http://dx.doi.org/10.3390/math7030228.

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In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures.

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31

Markin, Marat V., and Olivia B. Soghomonian. "On a Characterization of Convergence in Banach Spaces with a Schauder Basis." International Journal of Mathematics and Mathematical Sciences 2021 (September 30, 2021): 1–5. http://dx.doi.org/10.1155/2021/1640183.

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We extend the well-known characterizations of convergence in the spaces l p ( 1 ≤ p < ∞ ) of p -summable sequences and c 0 of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space c of convergent sequences.“The method in the present paper is abstract and is phrased in terms of Banach spaces, linear operators, and so on. This has the advantage of greater simplicity in proof and greater generality in applications.” Jacob T. Schwartz

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32

Marian Jakszto. "Another Proof That L^p-Bounded Pointwise Convergence Implies Weak Convergence." Real Analysis Exchange 36, no. 2 (2011): 479. http://dx.doi.org/10.14321/realanalexch.36.2.0479.

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33

Yapalı, Reha, and Utku Gürdal. "Pringsheim and statistical convergence for double sequences on $ L- $fuzzy normed space." AIMS Mathematics 6, no. 12 (2021): 13726–33. http://dx.doi.org/10.3934/math.2021796.

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<abstract><p>In this paper, we study the concept of statistical convergence for double sequences on $ L- $fuzzy normed spaces. Then we give a useful characterization on the statistical convergence of double sequences with respect to their convergence in the classical sense and we illustrate that our method of convergence is weaker than the usual convergence for double sequences on $ L- $fuzzy normed spaces.</p></abstract>

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34

Pratelli, Luca, and Pietro Rigo. "Convergence in Total Variation of Random Sums." Mathematics 9, no. 2 (January 19, 2021): 194. http://dx.doi.org/10.3390/math9020194.

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Let (Xn) be a sequence of real random variables, (Tn) a sequence of random indices, and (τn) a sequence of constants such that τn→∞. The asymptotic behavior of Ln=(1/τn)∑i=1TnXi, as n→∞, is investigated when (Xn) is exchangeable and independent of (Tn). We give conditions for Mn=τn(Ln−L)⟶M in distribution, where L and M are suitable random variables. Moreover, when (Xn) is i.i.d., we find constants an and bn such that supA∈B(R)|P(Ln∈A)−P(L∈A)|≤an and supA∈B(R)|P(Mn∈A)−P(M∈A)|≤bn for every n. In particular, Ln→L or Mn→M in total variation distance provided an→0 or bn→0, as it happens in some situations.

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35

Patterson, Richard, and Ekrem Savaş. "Double sequence transformations that guarantee a given rate of p-convergence." Filomat 25, no. 2 (2011): 129–35. http://dx.doi.org/10.2298/fil1102129p.

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In this paper the following sequence space is presented. Let [t] be a positive double sequence and define the sequence space ?''(t) = {complex sequences x : xk,l = O(tk,l)}. The set of geometrically dominated double sequences is defined as G'' = U r,s?(0,1) G(r, s) where G(r, s) = {complex sequences x : x k,l = O(rk sl)} for each r, s in the interval (0, 1). Using this definition, four dimensional matrix characterizations of l?,?, c'', and c0'' into G'' and into ?''(t) are presented. In addition to these definitions and characterizations it should be noted that this ensure a rate of converges of at least as fast as [t]. Other natural implications will also be presented.

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36

Rybkin, A. V. "Convergence of arguments of Blaschke products in $L\sb p$-metrics." Proceedings of the American Mathematical Society 111, no. 3 (March 1, 1991): 701. http://dx.doi.org/10.1090/s0002-9939-1991-1010000-3.

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37

Gát, G., and R. Toledo. "L p -norm convergence of series in compact, totally disconnected groups." Analysis Mathematica 22, no. 1 (March 1996): 13–24. http://dx.doi.org/10.1007/bf02342335.

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38

Yuan, Haiyan, and Cheng Song. "Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/679075.

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This paper introduces the stability and convergence of two-step Runge-Kutta methods with compound quadrature formula for solving nonlinear Volterra delay integro-differential equations. First, the definitions of(k,l)-algebraically stable and asymptotically stable are introduced; then the asymptotical stability of a(k,l)-algebraically stable two-step Runge-Kutta method with0<k<1is proved. For the convergence, the concepts ofD-convergence, diagonally stable, and generalized stage order are firstly introduced; then it is proved by some theorems that if a two-step Runge-Kutta method is algebraically stable and diagonally stable and its generalized stage order isp, then the method with compound quadrature formula isD-convergent of order at leastmin{p,ν}, whereνdepends on the compound quadrature formula.

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39

Shakh-Emirov, Tadgidin. "On uniform convergence of Fourier-Sobolev series." Daghestan Electronic Mathematical Reports, no. 12 (December 5, 2019): 55–61. http://dx.doi.org/10.31029/demr.12.5.

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Let $\{\varphi_{k}\}_{k=0}^\infty$ be a system of functions defined on $ [a, b] $ and orthonormal in $ L ^ 2_ \rho = L ^ 2_\rho ( a, b) $ with respect to the usual inner product. For a given positive integer $ r $, by $\{\varphi_{r,k}\}_{k=0}^\infty$ we denote the system of functions orthonormal with respect to the Sobolev-type inner product and generated by the system $\{\varphi_{k}\}_{k=0}^\infty$. In this paper, we study the question of the uniform convergence of the Fourier series by the system of functions $\{\varphi_{r,k}\}_{k=0}^\infty$ to the functions $f\in W^r_{L^p_\rho}$ in the case when the original system $\{\varphi_{k}\}_{k=0}^\infty$ forms a basis in the space $L^p_\rho=L^p_\rho(a,b)$ ($1\le p$, $p\neq2$).

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40

Ciampa, Gennaro, Gianluca Crippa, and Stefano Spirito. "Strong Convergence of the Vorticity for the 2D Euler Equations in the Inviscid Limit." Archive for Rational Mechanics and Analysis 240, no. 1 (March 1, 2021): 295–326. http://dx.doi.org/10.1007/s00205-021-01612-z.

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AbstractIn this paper we prove the uniform-in-time $$L^p$$ L p convergence in the inviscid limit of a family $$\omega ^\nu $$ ω ν of solutions of the 2D Navier–Stokes equations towards a renormalized/Lagrangian solution $$\omega $$ ω of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $$\omega ^{\nu }$$ ω ν to $$\omega $$ ω in $$L^p$$ L p . Finally, we show that solutions of the Euler equations with $$L^p$$ L p vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.

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41

Jabar, Asawer, and Noori Al-Mayahi. "Some Properties Related With L^0 (Ω,F,μ) Space." Al-Qadisiyah Journal Of Pure Science 25, no. 2 (March 31, 2020): 22–26. http://dx.doi.org/10.29350/qjps.2020.25.2.1059.

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The purpose of this paper is to investigate elementary properties of these measure and relation between these measure and we define a metric functions on the space of measurable functions and defined on finite measure space and we call the topology induced by p the topology of convergence in measure and we investigate now the connection between the convergence in metric of X and convergence in measure .

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42

Karanjgaokar, Varsha. "On the Rate of Convergence of Wavelet Expansions." Journal of the Indian Mathematical Society 85, no. 1-2 (January 4, 2018): 100. http://dx.doi.org/10.18311/jims/2018/14929.

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In this paper we estimate the rate of convergence of wavelet expansion of functions <em>f</em> ∈ <em>L<sup>p</sup></em>, 1 ≤ <em>p</em> ≤ ∞ at a point x. The pointwise and <em>L<sup>p</sup></em> results were obtained by Kelly, S. [4]. Our result generalizes her result.

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43

Liu, Yang, and Yoichiro Mori. "$L^p$ Convergence of the Immersed Boundary Method for Stationary Stokes Problems." SIAM Journal on Numerical Analysis 52, no. 1 (January 2014): 496–514. http://dx.doi.org/10.1137/130911329.

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44

Kusuoka, Seiichiro, and Ichiro Shigekawa. "Exponential convergence of Markovian semigroups and their spectra on $L^{p}$ -spaces." Kyoto Journal of Mathematics 54, no. 2 (2014): 367–99. http://dx.doi.org/10.1215/21562261-2642431.

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45

KOVAČ, VJEKOSLAV. "Quantitative norm convergence of double ergodic averages associated with two commuting group actions." Ergodic Theory and Dynamical Systems 36, no. 3 (November 6, 2014): 860–74. http://dx.doi.org/10.1017/etds.2014.87.

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We study double averages along orbits for measure-preserving actions of$\mathbb{A}^{{\it\omega}}$, the direct sum of countably many copies of a finite abelian group$\mathbb{A}$. We show an$\text{L}^{p}$norm-variation estimate for these averages, which in particular re-proves their convergence in$\text{L}^{p}$for any finite$p$and for any choice of two$\text{L}^{\infty }$functions. The result is motivated by recent questions on quantifying convergence of multiple ergodic averages.

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46

Henke, C., and L. Angermann. "L (L )-boundedness and convergence of DG(p) solutions for nonlinear conservation laws with boundary conditions." IMA Journal of Numerical Analysis 34, no. 4 (October 17, 2013): 1598–624. http://dx.doi.org/10.1093/imanum/drt047.

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47

Sheikh, Neyaz Ahmad, and Ab Hamid Ganie. "Some matrix transformations and almost convergence." Kathmandu University Journal of Science, Engineering and Technology 8, no. 2 (January 3, 2013): 89–92. http://dx.doi.org/10.3126/kuset.v8i2.7330.

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The sequence space bv(u,p) has been defined and the classes (bv(u,p):l?), (bv(u,p):c),and (bv(u,p):c0) of infinite matrices have been characterized by Ba?ar, Altay and Mursaleen ( see, [2] ). The main purposes of the present paper is to characterize the classes (bv(u,p):ƒ?),(bv(u, p):ƒ), and (bv(u,p):ƒ0), where ƒ?, ƒ, and ƒ0 denotes the spaces of almost bounded sequences, almost convergent sequences and almost convergent null sequences, respectively, with real or complex terms. Kathmandu University Journal of Science, Engineering and Technology Vol. 8, No. II, December, 2012, 89-92 DOI: http://dx.doi.org/10.3126/kuset.v8i2.7330

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48

Assani, I. "Minimal convergence on Lp spaces." Ergodic Theory and Dynamical Systems 10, no. 3 (September 1990): 411–20. http://dx.doi.org/10.1017/s0143385700005666.

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AbstractLet (X, F, μ) be a probability measure space, p and β real numbers such that 1≤p<+∞ and 0<β<p. For any linear positive operator T satisfying T1, T*1 = 1 we prove the norm and pointwise convergence of the sequence We get then the pointwise and norm convergence in Lp, 0 < β ≥ 1 < p < 2, of the sequence sgn Sif for any positive linear operator on Lp(Ω, A, μ) (μ-σ-finite) verifying ∥(1 − α)I + αS∥p ≤ 1 for a real number 0 < α < 1. In the particular case α = 1, (S is a contraction), β = p−l, this result gives the pointwise and norm convergence of the sequences introduced by Beauzamy and Enflo in 1985 to the asymptotic center of the sequence .

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49

Chan, DCN, AK-H. Chung, J. Haines, EH-T. Yau, and C.-C. Kuo. "The Accuracy of Optical Scanning: Influence of Convergence and Die Preparation." Operative Dentistry 36, no. 5 (October 1, 2011): 486–91. http://dx.doi.org/10.2341/10-067-l.

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SUMMARY The purpose of this study was to determine the reliability of the data acquisition and modeling process of laser and white light scanners by evaluating the reproducibility of digitized simulated crowns with different convergences. A secondary purpose was to analyze the influence of die preparation by testing this hypothesis with a set of dies without ditching compared with a set with well-defined margins. Ditching or trimming the die defines the position of the margin and acts as a guide to gingival contour when the restoration is being waxed. Two light scanners (a white light optical scanner [Steinbichler Gmbh, Neubeuern, Germany] and red laser light scanner [TurboDent System, Taichung, Taiwan]) were evaluated. Two sets of simulated crowns were fabricated as cone frustrum models with a total occlusal convergence (TOC) of 0°, 5°, 10°, 15°, 20°, and 25° and a 9-mm base and 3-mm height using a precision milling machine and computer-aided design/computer-aided manufacturing (CAD/CAM) technique. One set of the dies was ditched immediately below the finish line to enhance marginal definition. Each die was optically digitized five times directly with the two different measuring systems. The area of each triangle in the scan that is occlusal to the margin line was calculated and summed to produce the final surface area measurement provided. The digitizing error was compared with the computed surface area of the original master die sets and compared with a paired t-test (df=4; 95% CI). There was no difference in accuracy of the untrimmed dies between the two systems evaluated. We also did not find any difference in the 0° (p=0.12) and 5° degree (p=0.21) groups among the ditched dies. However, when the TOC exceeded 5°, there was a significant difference between the two groups, with the laser groups having a smaller error percentage. Three-dimensional light scanning was not affected by the convergence angle except in the 0°-5° range. Trimming the dies greatly affected the accuracy of scanning.

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50

Kayumov, I. R., and A. V. Kayumova. "Convergence of the Imaginary Parts of Simplest Fractions in L p ( ℝ ) for p < 1." Journal of Mathematical Sciences 202, no. 4 (September 23, 2014): 553–59. http://dx.doi.org/10.1007/s10958-014-2062-1.

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