Lp Spaces in vector lattices and applications

Abstract Lp spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian motion and the Brownian bridge are studied, to solve some stochastic differential equations.

[1]  D. Nualart,et al.  Fractional Brownian motion , 2006 .

[2]  Carlo Bardaro,et al.  Nonlinear integral operators and applications , 2003 .

[3]  A. Zaanen.  Riesz Spaces, II , 1983 .

[4]  J. Norris.  Appendix: probability and measure , 1997 .

[5]  A. R. Sambucini,et al.  Filter Convergence and Decompositions for Vector Lattice-Valued Measures , 2014, 1401.7818.

[6]  Julian Musielak,et al.  Orlicz Spaces and Modular Spaces , 1983 .

[7]  Quadratic Variation of Martingales in Riesz Spaces , 2014 .

[8]  A. Boccuto,et al.  Modular filter convergence theorems for Urysohn integral operators and applications , 2013 .

[9]  A. R. Sambucini,et al.  Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes , 2014, 1401.7835.

[10]  P. Butzer,et al.  The Mellin–Parseval formula and its interconnections with the exponential sampling theorem of optical physics , 2016 .

[11]  Richard B. Holmes,et al.  MATHEMATICAL FOUNDATIONS OF SIGNAL PROCESSING , 1979 .

[12]  Adriano M. Garsia,et al.  A Real Variable Lemma and the Continuity of Paths of Some Gaussian Processes , 1970 .

[13]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[14]  Gianluca Vinti,et al.  Approximation in variation by homothetic operators in multidimensional setting , 2013 .

[15]  Mohamed A. Khamsi,et al.  Modular function spaces , 1988 .

[16]  Lech Maligranda.  A simple proof of the Hölder and the Minkowski inequality , 1995 .

[17]  On the decompositions of $$T$$T-quasi-martingales on Riesz spaces , 2014 .

[18]  A. R. Sambucini,et al.  Order-type Henstock and McShane integrals in banach lattice setting , 2014, 2014 IEEE 12th International Symposium on Intelligent Systems and Informatics (SISY).

[19]  Gianluca Vinti,et al.  Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces , 2009, J. Approx. Theory.

[20]  Antonio Boccuto,et al.  Integral and ideals in Riesz spaces , 2009, Inf. Sci..

[21]  Paul L. Butzer,et al.  Fourier analysis and approximation , 1971 .

[22]  A. Boccuto,et al.  Differential Calculus in Riesz Spaces and Applications to g-Calculus , 2011 .

[23]  C. Bardaroa,et al.  Modular filter convergence theorems for abstract sampling type operators , 2014 .

[24]  Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures , 2015, 1503.08285.

[25]  J. Grobler.  Jensen’s and martingale inequalities in Riesz spaces , 2014 .

[26]  R. L. Stens,et al.  Kantorovich-Type Generalized Sampling Series in the Setting of Orlicz Spaces , 2007 .

[27]  A. Boccuto,et al.  Modular filter convergence theorems for abstract sampling type operators , 2013 .

[28]  W. Filter.  Representations of Archimedean Riesz Spaces A Survey , 1994 .

[29]  Achille Basile,et al.  Completeness of Lp-Spaces in the Finitely Additive Setting and Related Stories , 2000 .

[30]  Gianluca Vinti,et al.  Approximation with Respect to Goffman–Serrin Variation by Means of Non-Convolution Type Integral Operators , 2010 .

[31]  A. Banerjee,et al.  I-Completeness in Function Spaces , 2017, Tatra Mountains Mathematical Publications.

[32]  D. Costarelli,et al.  Order of approximation for sampling Kantorovich operators , 2014 .

[33]  M. Rao,et al.  Theory of Orlicz spaces , 1991 .

[34]  Paola Cavaliere,et al.  Functions determining locally solid topological Riesz spaces continuously embedded in $L^0$ , 2015 .

[35]  A. Boccuto,et al.  Convergence Theorems for Lattice Group-Valued Measures , 2018 .

[36]  G. Letta.  Martingales et intégration stochastique , 1984 .

[37]  Gianluca Vinti,et al.  A unifying approach to convergence of linear sampling type operators in Orlicz spaces , 2011 .

[38]  Gianluca Vinti,et al.  Enhancement of thermographic images as tool for structural analysis in earthquake engineering , 2015 .

[39]  R. L. Stens,et al.  Prediction by Samples From the Past With Error Estimates Covering Discontinuous Signals , 2010, IEEE Transactions on Information Theory.

[40]  A. R. Sambucini,et al.  Comparison between different types of abstract integrals in Riesz spaces , 1997 .

[41]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[42]  J. Wright,et al.  The measure extension problem for vector lattices , 1971 .

[43]  The Itô integral for Brownian motion in vector lattices. Part 2 , 2015 .

[44]  Paul L. Butzer,et al.  Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals , 2006 .

[45]  A. Boccuto,et al.  Modular Convergence Theorems for Integral Operators in the Context of Filter Exhaustiveness and Applications , 2013 .

[46]  P. Butzer,et al.  The Foundations of Fractional Calculus in the Mellin Transform Setting with Applications , 2015 .

[47]  J. Cooper.  Riesz spaces , 2012 .