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Journal articles on the topic 'Infinte products'

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Published: 4 June 2021

Last updated: 7 February 2022

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1

ELDAR, YONINA C., and TOBIAS WERTHER. "GENERAL FRAMEWORK FOR CONSISTENT SAMPLING IN HILBERT SPACES." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 03 (September 2005): 347–59. http://dx.doi.org/10.1142/s0219691305000890.

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We introduce a general framework for consistent linear reconstruction in infinite-dimensional Hilbert spaces. We study stable reconstructions in terms of Riesz bases and frames, and generalize the notion of oblique dual frames to infinte-dimensional frames. As we show, the linear reconstruction scheme coincides with the so-called oblique projection, which turns into an ordinary orthogonal projection when adapting the inner product. The inner product of interest is, in general, not unique. We characterize the inner products and the corresponding positive operators for which this geometrical interpretation applies.

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2

Jeong, JA A., Kazunori Kodaka, and Hiroyuki Osaka. "Purely Infinite Simple C*-Crossed Products II." Canadian Mathematical Bulletin 39, no. 2 (June 1, 1996): 203–10. http://dx.doi.org/10.4153/cmb-1996-025-2.

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AbstractWe study the pure infiniteness of C* -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C*-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C*-crossed products A ×αZ by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C*-algebra A ×α G is purely infinite.

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3

Loeb, Peter A., and David A. Ross. "Infinite products of infinite measures." Illinois Journal of Mathematics 49, no. 1 (January 2005): 153–58. http://dx.doi.org/10.1215/ijm/1258138311.

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4

Meier, John. "The topology of graph products of groups." Proceedings of the Edinburgh Mathematical Society 37, no. 3 (October 1994): 539–44. http://dx.doi.org/10.1017/s001309150001899x.

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Given a finite (connected) simplicial graph with groups assigned to the vertices, the graph product of the vertex groups is the free product modulo the relation that adjacent groups commute. The graph product of finitely presented infinite groups is both semistable at infinity and quasi-simply filtrated. Explicit bounds for the isoperimetric inequality and isodiametric inequality for graph products is given, based on isoperimetric and isodiametric inequalities for the vertex groups.

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5

Magnot, Jean-Pierre. "The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures." Journal of Mathematics 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/9853672.

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One of the goals of this article is to describe a setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure and of the concentration property on metric measured spaces, inspired from classical examples of means. In some cases, we get a linear extension of the limit at infinity. Then, the mean value on an infinite product is defined, first for cylindrical functions and secondly taking the uniform limit. Finally, the mean value for the heuristic Lebesgue measure on a separable infinite dimensional topological vector space (e.g., on a Hilbert space) is defined. This last object, which is not the classical infinite dimensional Lebesgue measure but its “normalized” version, is shown to be invariant under translation, scaling, and restriction.

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6

Brown, K. A. "INFINITE CROSSED PRODUCTS." Bulletin of the London Mathematical Society 22, no. 4 (July 1990): 394–96. http://dx.doi.org/10.1112/blms/22.4.394.

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7

Meir, Nadav. "Infinite lexicographic products." Annals of Pure and Applied Logic 173, no. 1 (January 2022): 102991. http://dx.doi.org/10.1016/j.apal.2021.102991.

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8

Izuchi, Keiji. "Weak infinite products of Blaschke products." Proceedings of the American Mathematical Society 129, no. 12 (April 16, 2001): 3611–18. http://dx.doi.org/10.1090/s0002-9939-01-05957-3.

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9

Muthuvel, Kandasamy. "Infinite products of alephs." Fundamenta Mathematicae 131, no. 3 (1988): 255–56. http://dx.doi.org/10.4064/fm-131-3-255-256.

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10

HANCL, JAROSLAV, and ONDREJ KOLOUCH. "Irrationality of infinite products." Publicationes Mathematicae Debrecen 83, no. 4 (December 1, 2013): 667–81. http://dx.doi.org/10.5486/pmd.2013.5676.

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11

Desbrow, Darrell. "96.15 Three infinite products." Mathematical Gazette 96, no. 535 (March 2012): 130–31. http://dx.doi.org/10.1017/s0025557200004150.

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12

Short, L. "Some further infinite products." International Journal of Mathematical Education in Science and Technology 24, no. 1 (January 1993): 91–99. http://dx.doi.org/10.1080/0020739930240112.

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13

Dehornoy, Patrick. "Infinite products in monoids." Semigroup Forum 34, no. 1 (December 1986): 21–68. http://dx.doi.org/10.1007/bf02573152.

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14

Toyoizumi, Masao. "On certain infinite products III." Acta Arithmetica 51, no. 3 (1988): 221–31. http://dx.doi.org/10.4064/aa-51-3-221-231.

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15

Trench, William F. "Conditional Convergence of Infinite Products." American Mathematical Monthly 106, no. 7 (August 1999): 646. http://dx.doi.org/10.2307/2589494.

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16

Tachiya, Yohei. "Transcendence of certain infinite products." Journal of Number Theory 125, no. 1 (July 2007): 182–200. http://dx.doi.org/10.1016/j.jnt.2006.11.006.

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17

Stephens, E. "79.52 Slowly Convergent Infinite Products." Mathematical Gazette 79, no. 486 (November 1995): 561. http://dx.doi.org/10.2307/3618092.

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18

DUKE, WILLIAM, and HA NAM NGUYEN. "INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS." Bulletin of the Australian Mathematical Society 91, no. 3 (February 26, 2015): 400–411. http://dx.doi.org/10.1017/s0004972715000039.

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We study analytic properties of certain infinite products of cyclotomic polynomials that generalise some products introduced by Mahler. We characterise those that have the unit circle as a natural boundary and use associated Dirichlet series to obtain their asymptotic behaviour near roots of unity.

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19

Trench, William F. "Conditional Convergence of Infinite Products." American Mathematical Monthly 106, no. 7 (August 1999): 646–51. http://dx.doi.org/10.1080/00029890.1999.12005098.

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20

Montgomery, Susan. "Book Review: Infinite crossed products." Bulletin of the American Mathematical Society 24, no. 2 (April 1, 1991): 391–403. http://dx.doi.org/10.1090/s0273-0979-1991-16044-1.

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21

Campbell, Geoffrey B. "Infinite products over hyperpyramid lattices." International Journal of Mathematics and Mathematical Sciences 23, no. 4 (2000): 271–77. http://dx.doi.org/10.1155/s0161171200000764.

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22

Budzyńska, Monika, and Simeon Reich. "Infinite products of holomorphic mappings." Abstract and Applied Analysis 2005, no. 4 (2005): 327–41. http://dx.doi.org/10.1155/aaa.2005.327.

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LetXbe a complex Banach space,𝒩a norming set forX, andD⊂Xa bounded, closed, and convex domain such that its norm closureD¯is compact inσ(X,𝒩). Let∅≠C⊂Dlie strictly insideD. We study convergence properties of infinite products of those self-mappings ofCwhich can be extended to holomorphic self-mappings ofD. Endowing the space of sequences of such mappings with an appropriate metric, we show that the subset consisting of all the sequences with divergent infinite products isσ-porous.

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23

Rohm, Dale M. "Products of infinite-dimensional spaces." Proceedings of the American Mathematical Society 108, no. 4 (April 1, 1990): 1019. http://dx.doi.org/10.1090/s0002-9939-1990-0946625-x.

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24

Ibrahim, Adel K., and Medhat A. Rakha. "Numerical computations of infinite products." Applied Mathematics and Computation 161, no. 1 (February 2005): 271–83. http://dx.doi.org/10.1016/j.amc.2003.12.027.

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25

Knopfmacher, Arnold, and John Knopfmacher. "Infinite products for power series." Journal of Approximation Theory 59, no. 3 (December 1989): 276–81. http://dx.doi.org/10.1016/0021-9045(89)90091-9.

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26

Hua, Fan Ai. "Multifractal analysis of infinite products." Journal of Statistical Physics 86, no. 5-6 (March 1997): 1313–36. http://dx.doi.org/10.1007/bf02183625.

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27

Miranda, Enrique, and Marco Zaffalon. "Independent products in infinite spaces." Journal of Mathematical Analysis and Applications 425, no. 1 (May 2015): 460–88. http://dx.doi.org/10.1016/j.jmaa.2014.12.049.

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28

Giordano, Thierry, and Adam Sierakowski. "Purely infinite partial crossed products." Journal of Functional Analysis 266, no. 9 (May 2014): 5733–64. http://dx.doi.org/10.1016/j.jfa.2014.02.025.

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29

Zucker, I. J. "A systematic way of converting infinite series into infinite products." Journal of Physics A: Mathematical and General 20, no. 1 (January 11, 1987): L13—L17. http://dx.doi.org/10.1088/0305-4470/20/1/003.

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30

Dydak, Jerzy. "Extension theory of infinite symmetric products." Fundamenta Mathematicae 182, no. 1 (2004): 53–77. http://dx.doi.org/10.4064/fm182-1-3.

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31

Campbell, Geoffrey B. "Infinite products over visible lattice points." International Journal of Mathematics and Mathematical Sciences 17, no. 4 (1994): 637–54. http://dx.doi.org/10.1155/s0161171294000918.

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About fifty new multivariate combinatorial identities are given, connected with partition theory, prime products, and Dirichlet series. Connections to Lattice Sums in Chemistry and Physics are alluded to also.

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32

Alaca, Ayşe, Şaban Alaca, and Kenneth S. Williams. "Some Infinite Products of Ramanujan Type." Canadian Mathematical Bulletin 52, no. 4 (December 1, 2009): 481–92. http://dx.doi.org/10.4153/cmb-2009-050-5.

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33

Jeong, Ja A. "Purely Infinite Simple C ∗ -Crossed Products." Proceedings of the American Mathematical Society 123, no. 10 (October 1995): 3075. http://dx.doi.org/10.2307/2160662.

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34

Toyoizumi, Masao. "A note on certain infinite products." Proceedings of the Japan Academy, Series A, Mathematical Sciences 68, no. 10 (1992): 345–47. http://dx.doi.org/10.3792/pjaa.68.345.

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35

Krupski, Mikołaj. "On functional tightness of infinite products." Topology and its Applications 229 (September 2017): 141–47. http://dx.doi.org/10.1016/j.topol.2017.07.013.

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36

Amou, Masaaki, and Keijo Väänänen. "Arithmetical properties of certain infinite products." Journal of Number Theory 153 (August 2015): 283–303. http://dx.doi.org/10.1016/j.jnt.2015.01.011.

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37

Borges, Carlos R. "The sup metric on infinite products." Bulletin of the Australian Mathematical Society 44, no. 3 (December 1991): 461–66. http://dx.doi.org/10.1017/s0004972700029956.

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We study the properties of the sup metric on infinite products Z = X.(If d is a bounded metric on X then ρ, defined by ρ((xα), (yα)) = , is the sup metric on Z.) In particular, we prove that if X is an AR(metric) or a topological group then so is Z.

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38

Hanna, Yousry S., and Samya F. Ragheb. "On the Infinite Products of Matrices." Advances in Pure Mathematics 02, no. 05 (2012): 349–53. http://dx.doi.org/10.4236/apm.2012.25050.

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39

Wermuth, Edgar M. E. "Some Elementary Properties of Infinite Products." American Mathematical Monthly 99, no. 6 (June 1992): 530. http://dx.doi.org/10.2307/2324060.

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40

Power, S. C. "Infinite Lexicographic Products of Triangular Algebras." Bulletin of the London Mathematical Society 27, no. 3 (May 1995): 273–77. http://dx.doi.org/10.1112/blms/27.3.273.

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41

Allouche, Jean-Paul, and Henri Cohen. "Dirichlet Series and Curious infinite Products." Bulletin of the London Mathematical Society 17, no. 6 (November 1985): 531–38. http://dx.doi.org/10.1112/blms/17.6.531.

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42

Wermuth, Edgar M. E. "Some Elementary Properties of Infinite Products." American Mathematical Monthly 99, no. 6 (June 1992): 530–37. http://dx.doi.org/10.1080/00029890.1992.11995887.

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43

Trench, William F. "Invertibly convergent infinite products of matrices." Journal of Computational and Applied Mathematics 101, no. 1-2 (January 1999): 255–63. http://dx.doi.org/10.1016/s0377-0427(98)00191-5.

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44

Kimura, Shun-ichi, and Angelo Vistoli. "Chow rings of infinite symmetric products." Duke Mathematical Journal 85, no. 2 (November 1996): 411–30. http://dx.doi.org/10.1215/s0012-7094-96-08517-8.

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45

Chmielewska, Katarzyna, and Aleksander Maliszewski. "Infinite products of Borel measurable functions." Topology and its Applications 155, no. 17-18 (October 2008): 1996–2000. http://dx.doi.org/10.1016/j.topol.2007.04.027.

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46

Chmielewska, Katarzyna, and Aleksander Maliszewski. "Infinite products of quasi-continuous functions." Topology and its Applications 156, no. 18 (December 2009): 3101–8. http://dx.doi.org/10.1016/j.topol.2009.03.048.

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47

Guu, Sy-Ming, Yung-Yih Lur, and Chin-Tzong Pang. "On Infinite Products of Fuzzy Matrices." SIAM Journal on Matrix Analysis and Applications 22, no. 4 (January 2001): 1190–203. http://dx.doi.org/10.1137/s0895479800366021.

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48

Boyer, Robert P., and Yun S. Yoo. "Unitary representations of infinite wreath products." Annals of Functional Analysis 10, no. 1 (February 2019): 97–105. http://dx.doi.org/10.1215/20088752-2018-0011.

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49

Pustylnik, Evgeniy, Simeon Reich, and Alexander J. Zaslavski. "Inexact Infinite Products of Nonexpansive Mappings." Numerical Functional Analysis and Optimization 30, no. 5-6 (June 30, 2009): 632–45. http://dx.doi.org/10.1080/01630560902987998.

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50

Wang, Xingping, and Zhaolin Cheng. "Infinite products of uniformly paracontracting matrices." Linear and Multilinear Algebra 64, no. 5 (July 8, 2015): 856–62. http://dx.doi.org/10.1080/03081087.2015.1063577.

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