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Journal articles on the topic 'Blaschke products'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2024

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1

Marshall, Donald, and Arne Stray. "Interpolating Blaschke products." Pacific Journal of Mathematics 173, no. 2 (April 1, 1996): 491–99. http://dx.doi.org/10.2140/pjm.1996.173.491.

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2

Cochran, W. George. "Random Blaschke products." Transactions of the American Mathematical Society 322, no. 2 (February 1, 1990): 731–55. http://dx.doi.org/10.1090/s0002-9947-1990-1022163-8.

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3

GORKIN, PAMELA, and RAYMOND MORTINI. "Universal Blaschke products." Mathematical Proceedings of the Cambridge Philosophical Society 136, no. 1 (January 2004): 175–84. http://dx.doi.org/10.1017/s0305004103007023.

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4

Kraus, Daniela, and Oliver Roth. "Maximal Blaschke products." Advances in Mathematics 241 (July 2013): 58–78. http://dx.doi.org/10.1016/j.aim.2013.03.017.

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5

Heittokangas, Janne. "On Interpolating Blaschke Products and Blaschke-Oscillatory Equations." Constructive Approximation 34, no. 1 (May 12, 2010): 1–21. http://dx.doi.org/10.1007/s00365-010-9100-0.

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6

Jevtić, Miroljub. "Blaschke products in Lipschitz spaces." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (September 23, 2009): 689–705. http://dx.doi.org/10.1017/s001309150700065x.

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AbstractWe study the membership of Blaschke products in Lipschitz spaces, especially for interpolating Blaschke products and for those whose zeros lie in a Stolz angle. We prove several theorems that complement or extend the earlier works of Ahern and the author.

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7

Chalendar, Isabelle, and Raymond Mortini. "When do finite Blaschke products commute?" Bulletin of the Australian Mathematical Society 64, no. 2 (October 2001): 189–200. http://dx.doi.org/10.1017/s0004972700039861.

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We study the following questions. Which finite Blaschke products are eigenvectors of the composition operatorsTu:f↦f∘u, what are the possible eigenvalues, and which pairs (B,C) of finite Blaschke products commute (that is, satisfyB∘C=C∘B).

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8

Garnett, John, and Artur Nicolau. "Interpolating Blaschke products generateH∞." Pacific Journal of Mathematics 173, no. 2 (April 1, 1996): 501–10. http://dx.doi.org/10.2140/pjm.1996.173.501.

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9

Izuchi, Keiji. "Factorization of Blaschke products." Michigan Mathematical Journal 40, no. 1 (1993): 53–75. http://dx.doi.org/10.1307/mmj/1029004674.

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10

Penrose, Chris, and Christian Beck. "Superstatistics of Blaschke products." Dynamical Systems 31, no. 1 (July 16, 2015): 89–105. http://dx.doi.org/10.1080/14689367.2015.1062978.

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11

ARTEAGA, CARLOS. "Commuting finite Blaschke products." Ergodic Theory and Dynamical Systems 19, no. 3 (June 1999): 549–52. http://dx.doi.org/10.1017/s0143385799130165.

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We consider the set of finite Blaschke products $F$ for which the fixed points on the circle $S^1$ are expanding and we prove that if $F'(x) \ne F'(y)$ for all different fixed points $x,y$ of $F$ on $S^1$, then $F$ commutes only with its own powers.

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12

Daepp, Ulrich, Pamela Gorkin, Andrew Shaffer, Benjamin Sokolowsky, and Karl Voss. "Decomposing finite Blaschke products." Journal of Mathematical Analysis and Applications 426, no. 2 (June 2015): 1201–16. http://dx.doi.org/10.1016/j.jmaa.2015.01.039.

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13

Nicolau, Artur. "Finite Products of Interpolating Blaschke Products." Journal of the London Mathematical Society 50, no. 3 (December 1994): 520–31. http://dx.doi.org/10.1112/jlms/50.3.520.

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14

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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15

Chalendar, Isabelle, Pamela Gorkin, and Jonathan R. Partington. "Boundary interpolation and approximation by infinite Blaschke products." MATHEMATICA SCANDINAVICA 107, no. 2 (December 1, 2010): 305. http://dx.doi.org/10.7146/math.scand.a-15157.

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This paper considers the problem of boundary interpolation (in the sense of non-tangential limits) by Blaschke products and interpolating Blaschke products. Simple and constructive proofs, which also work in the more general situation of $H^\infty(\Omega)$ where $\Omega$ is a more general domain, are given of a number of results showing the existence of Blaschke products solving certain interpolation problems at a countable set of points on the circle. A variant of Frostman's theorem is also presented.

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16

PUJALS, ENRIQUE R., and MICHAEL SHUB. "Dynamics of two-dimensional Blaschke products." Ergodic Theory and Dynamical Systems 28, no. 2 (April 2008): 575–85. http://dx.doi.org/10.1017/s0143385707000752.

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AbstractIn this paper we study the dynamics on $\mathbb {T}^2$ and $\mathbb {C}^2$ of a two-dimensional Blaschke product. We prove that in the case when the Blaschke product is a diffeomorphism of $\mathbb {T}^2$ with all periodic points hyperbolic then the dynamics is hyperbolic. If a two-dimensional Blaschke product diffeomorphism of $\mathbb {T}^2$ is embedded in a two-dimensional family given by composition with translations of $\mathbb {T}^2$, then we show that there is a non-empty open set of parameter values for which the dynamics is Anosov or has an expanding attractor with a unique SRB measure.

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17

VAN VLIET, DANIEL. "PROPERTIES OF A NONLINEAR BLASCHKE PRODUCT DECOMPOSITION ALGORITHM." Advances in Adaptive Data Analysis 01, no. 04 (October 2009): 529–42. http://dx.doi.org/10.1142/s1793536909000229.

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Motivated by developments in nonlinear time–space–frequency analysis such as Refs. 8 and 14, we investigate the properties of Blaschke products. Inner products are constructed under which certain sets of Blaschke products, each have a single zero location, form orthonormal bases for H2(D). Using these sets of Blaschke products as approximants, a greedy algorithm decomposition is implemented. Properties are observed which may help to develop a faster search type algorithm.

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18

Khemphet, Anchalee, and Justin R. Peters. "Semicrossed Products of the Disk Algebra and the Jacobson Radical." Canadian Mathematical Bulletin 57, no. 1 (March 14, 2014): 80–89. http://dx.doi.org/10.4153/cmb-2012-018-8.

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Abstract We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras. Furthermore, in the case that the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step, the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.

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19

FRICAIN, EMMANUEL, and JAVAD MASHREGHI. "INTEGRAL MEANS OF THE DERIVATIVES OF BLASCHKE PRODUCTS." Glasgow Mathematical Journal 50, no. 2 (May 2008): 233–49. http://dx.doi.org/10.1017/s0017089508004175.

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AbstractWe study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspaceKBgenerated by the Blaschke productB.

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20

LI, HONG, LUOQING LI, and YUAN Y. TANG. "MONO-COMPONENT DECOMPOSITION OF SIGNALS BASED ON BLASCHKE BASIS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (November 2007): 941–56. http://dx.doi.org/10.1142/s0219691307002130.

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This paper mainly focuses on decomposition of signals in terms of mono-component signals which are analytic with strictly increasing nonlinear phase. The properties of Blaschke basis and the approximation behavior of Blaschke basis expansions are studied. Each Blaschke product is analytic and mono-component. An explicit expression of the phase function of Blaschke product is given. The convergence results for Blaschke basis expansions show that it is suitable to approximate a signal by a linear combination of Blaschke products. Experiments are presented to illustrate the general theory.

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21

Rudin, Walter, and Peter Colwell. "Blaschke Products: Bounded Analytic Functions." American Mathematical Monthly 94, no. 3 (March 1987): 311. http://dx.doi.org/10.2307/2323409.

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22

Oyma, Knut. "Approximation by Interpolating Blaschke Products." MATHEMATICA SCANDINAVICA 79 (June 1, 1996): 255. http://dx.doi.org/10.7146/math.scand.a-12605.

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23

Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. "Ellipses and Finite Blaschke Products." American Mathematical Monthly 109, no. 9 (November 2002): 785. http://dx.doi.org/10.2307/3072367.

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24

Danikas, N., and Chr Mouratides. "Blaschke products in Qp spaces." Complex Variables, Theory and Application: An International Journal 43, no. 2 (December 2000): 199–209. http://dx.doi.org/10.1080/17476930008815311.

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25

Stray, Arne. "Minimal Interpolation by Blaschke Products." Journal of the London Mathematical Society s2-32, no. 3 (December 1985): 488–96. http://dx.doi.org/10.1112/jlms/s2-32.3.488.

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26

Matheson, Alec, and Timothy H. McNicholl. "Computable analysis and Blaschke products." Proceedings of the American Mathematical Society 136, no. 01 (January 1, 2008): 321–33. http://dx.doi.org/10.1090/s0002-9939-07-09102-2.

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27

Gau, Hwa-Long, and Pei Yuan Wu. "Finite Blaschke products of contractions." Linear Algebra and its Applications 368 (July 2003): 359–70. http://dx.doi.org/10.1016/s0024-3795(02)00697-3.

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28

Fujimura, Masayo. "Blaschke Products and Circumscribed Conics." Computational Methods and Function Theory 17, no. 4 (May 4, 2017): 635–52. http://dx.doi.org/10.1007/s40315-017-0201-7.

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29

Arteaga, Carlos. "Centralizers of finite Blaschke products." Boletim da Sociedade Brasileira de Matem�tica 31, no. 2 (June 2000): 163–73. http://dx.doi.org/10.1007/bf01244242.

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30

Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. "Ellipses and Finite Blaschke Products." American Mathematical Monthly 109, no. 9 (November 2002): 785–95. http://dx.doi.org/10.1080/00029890.2002.11919914.

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31

Fujimura, Masayo. "Inscribed Ellipses and Blaschke Products." Computational Methods and Function Theory 13, no. 4 (September 26, 2013): 557–73. http://dx.doi.org/10.1007/s40315-013-0037-8.

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32

Videnskii, I. V. "Multiple interpolation by Blaschke products." Journal of Soviet Mathematics 34, no. 6 (September 1986): 2139–43. http://dx.doi.org/10.1007/bf01741588.

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33

Chalendar, Isabelle, Pamela Gorkin, Jonathan R. Partington, and William T. Ross. "Clark measures and a theorem of Ritt." MATHEMATICA SCANDINAVICA 122, no. 2 (April 8, 2018): 277. http://dx.doi.org/10.7146/math.scand.a-104444.

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We determine when a finite Blaschke product $B$ can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for $B$. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute.

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34

Dubinin, V. N. "Critical Values of Finite Blaschke Products." Doklady Mathematics 104, no. 1 (July 2021): 163–64. http://dx.doi.org/10.1134/s1064562421040050.

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35

Izuchi, Kei Ji. "Zero sets of interpolating Blaschke products." Pacific Journal of Mathematics 119, no. 2 (October 1, 1985): 337–42. http://dx.doi.org/10.2140/pjm.1985.119.337.

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36

Stray, A. "Blaschke products and Nevanlinna-Pick interpolation." Publicacions Matemàtiques 59 (January 1, 2015): 45–54. http://dx.doi.org/10.5565/publmat_59115_03.

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37

Izuchi, Keiji. "Spreading blaschke products and homeomorphic parts." Complex Variables, Theory and Application: An International Journal 40, no. 4 (February 2000): 359–69. http://dx.doi.org/10.1080/17476930008815228.

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38

Guillory, Carroll, and Keiji Izuchi. "Interpolating blaschke products and nonanalytic sets." Complex Variables, Theory and Application: An International Journal 23, no. 3-4 (December 1993): 163–75. http://dx.doi.org/10.1080/17476939308814682.

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39

Craighead, R. L., and F. W. Carroll. "A decomposition of finite blaschke products." Complex Variables, Theory and Application: An International Journal 26, no. 4 (January 1995): 333–41. http://dx.doi.org/10.1080/17476939508814794.

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40

Stray, Arne. "Minimal Interpolation by Blaschke Products II." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 329–32. http://dx.doi.org/10.1112/blms/20.4.329.

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41

Nicolau, Artur. "Blaschke Products with Prescribed Radial Limits." Bulletin of the London Mathematical Society 23, no. 3 (May 1991): 249–55. http://dx.doi.org/10.1112/blms/23.3.249.

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42

Canela, Jordi, Núria Fagella, and Antonio Garijo. "Tongues in degree 4 Blaschke products." Nonlinearity 29, no. 11 (September 21, 2016): 3464–95. http://dx.doi.org/10.1088/0951-7715/29/11/3464.

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43

Izuchi, Keiji. "Interpolating Blaschke Products and Factorization Theorems." Journal of the London Mathematical Society 50, no. 3 (December 1994): 547–67. http://dx.doi.org/10.1112/jlms/50.3.547.

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44

Hjelle, Geir Arne. "Unimodular functions and interpolating Blaschke products." Proceedings of the American Mathematical Society 134, no. 1 (June 2, 2005): 207–14. http://dx.doi.org/10.1090/s0002-9939-05-07968-2.

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45

Gallardo-Gutiérrez, Eva A., and Pamela Gorkin. "Interpolating Blaschke products and angular derivatives." Transactions of the American Mathematical Society 364, no. 5 (May 1, 2012): 2319–37. http://dx.doi.org/10.1090/s0002-9947-2012-05535-8.

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46

GORKIN, PAMELA, and RAYMOND MORTINI. "VALUE DISTRIBUTION OF INTERPOLATING BLASCHKE PRODUCTS." Journal of the London Mathematical Society 72, no. 01 (July 20, 2005): 151–68. http://dx.doi.org/10.1112/s0024610705006411.

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47

Dyn, N., C. A. Micchelli, and T. J. Rivlin. "Blaschke products and optimal recovery inH ∞." Calcolo 24, no. 1 (March 1987): 1–21. http://dx.doi.org/10.1007/bf02576413.

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48

Jevtić, Miroljub. "On Blaschke products in Besov spaces." Journal of Mathematical Analysis and Applications 149, no. 1 (June 1990): 86–95. http://dx.doi.org/10.1016/0022-247x(90)90287-p.

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49

Gorkin, Pamela, and Raymond Mortini. "Cluster sets of interpolating Blaschke products." Journal d'Analyse Mathématique 96, no. 1 (December 2005): 369–95. http://dx.doi.org/10.1007/bf02787836.

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50

Izuchi, Keiji. "Weak infinite powers of Blaschke products." Journal d'Analyse Mathématique 75, no. 1 (December 1998): 135–54. http://dx.doi.org/10.1007/bf02788696.

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