Статті в журналах: "Produit de Blaschke"

1

Barza, Ilie, and Dorin Ghisa. "Blaschke product generated covering surfaces." Mathematica Bohemica 134, no. 2 (2009): 173–82. http://dx.doi.org/10.21136/mb.2009.140652.

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2

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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3

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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4

Vasylkiv, YA V., A. A. Kondratyuk, and S. I. Tarasyuk. "ON BOUNDEDNESS OF INTEGRAL MEANS OF BLASCHKE PRODUCT LOGARITHMS." Mathematical Modelling and Analysis 8, no. 3 (September 30, 2003): 259–65. http://dx.doi.org/10.3846/13926292.2003.9637228.

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Using the Fourier series method for the analytic functions, we obtain a result characterizing the behaviour of the integral means of Blaschke product logarithms. Namely, if the zero counting function n(r, B) of the Blaschke product B satisfies the conditionwhere l is a positive function on (0, 1) such thatthen the q‐integral mean mq (r, log B) = [] is bounded on (0,1), where log B is a branch of the logarithm of B. Šiame straipsnyje Furje eilučiu metodu gauta analitiniu funkciju Blaschke sandaugos logaritmu integraliniu reikšmiu elgsenos charakteristika. Jeigu Blaschke sandaugos B nuliu funkcija n(r, B) tenkina salyga [], čia l yra neneigiama funkcija intervale (0,1) ir [], tuomet q‐integraline reikšme [] yra aprežta intervale (0,1), kai log B yra B logaritmo šaka.

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5

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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6

Guillory, Carroll. "A Characterization of a Sparse Blaschke Product." Canadian Mathematical Bulletin 32, no. 4 (December 1, 1989): 385–90. http://dx.doi.org/10.4153/cmb-1989-056-0.

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AbstractWe give a characterization of a sparse Blaschke product b in terms of the separation of support sets of its zeros in M(H∞ + C) and the structure of the nonanalytic points. We use this characterization to give a sufficient condition on an interpolating Blaschke product q to have the following property: there exists a non trivial Gleason part P on which q is nonzero and less than one.

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7

Girela, Daniel, José Ángel Peláez, and Dragan Vukotić. "INTEGRABILITY OF THE DERIVATIVE OF A BLASCHKE PRODUCT." Proceedings of the Edinburgh Mathematical Society 50, no. 3 (October 2007): 673–87. http://dx.doi.org/10.1017/s0013091504001014.

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AbstractWe study the membership of derivatives of Blaschke products in Hardy and Bergman spaces, especially for the the interpolating Blaschke products and for those whose zeros lie in a Stolz domain. We obtain new and very simple proofs of some known results and prove new theorems that complement or extend the earlier works of Ahern, Clark, Cohn, Kim, Newman, Protas, Rudin, Vinogradov and others.

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8

Shamoyan, F. A., V. A. Bednazh, and V. A. Kustova. "Blaschke product in Privalov classes." Sibirskie Elektronnye Matematicheskie Izvestiya 18, no. 1 (March 5, 2021): 168–75. http://dx.doi.org/10.33048/semi.2021.18.014.

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9

Mashreghi, Javad. "Expanding a Finite Blaschke Product." Complex Variables, Theory and Application: An International Journal 47, no. 3 (March 2002): 255–58. http://dx.doi.org/10.1080/02781070290001418.

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10

Bogatyrev, A. B. "Blaschke product for bordered surfaces." Analysis and Mathematical Physics 9, no. 4 (February 13, 2019): 1877–86. http://dx.doi.org/10.1007/s13324-019-00284-z.

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11

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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12

Girela, Daniel, and José Ángel Peláez. "On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain." Canadian Mathematical Bulletin 49, no. 3 (September 1, 2006): 381–88. http://dx.doi.org/10.4153/cmb-2006-038-x.

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AbstractIt is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces Ap with 0 < p < 3/2. The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products B with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of B′ in the space Ap (p < 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B′ ∉ A3/2.

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13

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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14

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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15

Ballantine, Cristina, and Dorin Ghisa. "Colour visualization of Blaschke product mappings." Complex Variables and Elliptic Equations 55, no. 1-3 (January 2010): 201–17. http://dx.doi.org/10.1080/17476930902998944.

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16

Chen, Qiuhui, Tao Qian, Guangbin Ren, and Yi Wang. "B-splines of Blaschke product type." Computers & Mathematics with Applications 62, no. 10 (November 2011): 3669–81. http://dx.doi.org/10.1016/j.camwa.2011.09.002.

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17

Cerejeiras, Paula, Qiuhui Chen, and Uwe Kaehler. "Bedrosian Identity in Blaschke Product Case." Complex Analysis and Operator Theory 6, no. 1 (August 5, 2010): 275–300. http://dx.doi.org/10.1007/s11785-010-0092-3.

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18

MOGHADASI, S. REZA. "POLAR DECOMPOSITION OF THE k-FOLD PRODUCT OF LEBESGUE MEASURE ON ℝn". Bulletin of the Australian Mathematical Society 85, № 2 (6 січня 2012): 315–24. http://dx.doi.org/10.1017/s0004972711003273.

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AbstractThe Blaschke–Petkantschin formula is a geometric measure decomposition of the q-fold product of Lebesgue measure on ℝn. Here we discuss another decomposition called polar decomposition by considering ℝn×⋯×ℝn as ℳn×k and using its polar decomposition. This is a generalisation of the Blaschke–Petkantschin formula and may be useful when one needs to integrate a function g:ℝn×⋯×ℝn→ℝ with rotational symmetry, that is, for each orthogonal transformation O,g(O(x1),…,O(xk))=g(x1,…xk). As an application we compute the moments of a Gaussian determinant.

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19

Reijonen, Atte. "Remark on Integral Means of Derivatives of Blaschke Products." Canadian Mathematical Bulletin 61, no. 3 (September 1, 2018): 640–49. http://dx.doi.org/10.4153/cmb-2017-059-2.

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AbstractIf B is the Blachke product with zeros {zn}, then , whereMoreover, it is a well-known fact that, for 0 < p < ∞,is bounded if and only if Mp(r, ΨB) is bounded. We find a Blaschke product B0 such that Mp(r, ) and Mp(r, ) are not comparable for any < p < ∞. In addition, it is shown that, if 0 < p < ∞, B is a Carleson–Newman Blaschke product and a weight ω satisfies a certain regularity condition, thenwhere d A(z) is the Lebesgue area measure on the unit disc.

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20

Jensen, E. B. Vedel. "An induction proof of the generalized Blaschke-Petkantschin formula." Advances in Applied Probability 28, no. 2 (June 1996): 334. http://dx.doi.org/10.2307/1428044.

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The classical Blaschke-Petkanschin formula is a formula in integral geometry givmg a geometric measure decomposition of the q-fold product of Lebesgue measure. The original versions are due to Blaschke and Petkanschin in the 1930s. In Zähle (1990) and Jensen and Kiêu (1992), generalized versions have been derived, where Lebesgue measure is replaced by Hausdorff measure.

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21

Jensen, E. B. Vedel. "An induction proof of the generalized Blaschke-Petkantschin formula." Advances in Applied Probability 28, no. 02 (June 1996): 334. http://dx.doi.org/10.1017/s000186780004828x.

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Анотація:

The classical Blaschke-Petkanschin formula is a formula in integral geometry givmg a geometric measure decomposition of the q-fold product of Lebesgue measure. The original versions are due to Blaschke and Petkanschin in the 1930s. In Zähle (1990) and Jensen and Kiêu (1992), generalized versions have been derived, where Lebesgue measure is replaced by Hausdorff measure.

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22

Evdoridou, Vasiliki, Lasse Rempe, and David J. Sixsmith. "Fatou’s Associates." Arnold Mathematical Journal 6, no. 3-4 (October 26, 2020): 459–93. http://dx.doi.org/10.1007/s40598-020-00148-6.

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AbstractSuppose that f is a transcendental entire function, $$V \subsetneq {\mathbb {C}}$$ V ⊊ C is a simply connected domain, and U is a connected component of $$f^{-1}(V)$$ f - 1 ( V ) . Using Riemann maps, we associate the map $$f :U \rightarrow V$$ f : U → V to an inner function $$g :{\mathbb {D}}\rightarrow {\mathbb {D}}$$ g : D → D . It is straightforward to see that g is either a finite Blaschke product, or, with an appropriate normalisation, can be taken to be an infinite Blaschke product. We show that when the singular values of f in V lie away from the boundary, there is a strong relationship between singularities of g and accesses to infinity in U. In the case where U is a forward-invariant Fatou component of f, this leads to a very significant generalisation of earlier results on the number of singularities of the map g. If U is a forward-invariant Fatou component of f there are currently very few examples where the relationship between the pair (f, U) and the function g has been calculated. We study this relationship for several well-known families of transcendental entire functions. It is also natural to ask which finite Blaschke products can arise in this manner, and we show the following: for every finite Blaschke product g whose Julia set coincides with the unit circle, there exists a transcendental entire function f with an invariant Fatou component such that g is associated with f in the above sense. Furthermore, there exists a single transcendental entire function f with the property that any finite Blaschke product can be arbitrarily closely approximated by an inner function associated with the restriction of f to a wandering domain.

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23

Schipp, F., and J. Bokor. "Rational bases generated by blaschke product systems." IFAC Proceedings Volumes 36, no. 16 (September 2003): 1309–14. http://dx.doi.org/10.1016/s1474-6670(17)34941-8.

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24

Qing, Lin. "Imbedded operators with finite Blaschke product symbol." Acta Mathematica Sinica 6, no. 1 (March 1990): 72–79. http://dx.doi.org/10.1007/bf02108866.

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25

Dong, Xin-Han, Wen-Hui Ai, and Hai-Hua Wu. "The infinite range of infinite Blaschke product." Proceedings of the American Mathematical Society 148, no. 1 (July 1, 2019): 193–201. http://dx.doi.org/10.1090/proc/14672.

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26

Gullory, Carroll J. "Maximal subalgebra of Douglas algebra." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 735–41. http://dx.doi.org/10.1155/s0161171288000894.

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Whenqis an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebraBofH∞[q¯]to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products inB. If the setM(B)⋂Z(q)is not open inZ(q), we also find a condition that guarantees the existence of a factorq0ofqinH∞such thatBis maximal inH∞[q¯]. We also give conditions that show when two arbitrary Douglas algebrasAandB, withA⫅Bhave property thatAis maximal inB.

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27

Wegert, Elias. "Seeing the Monodromy Group of a Blaschke Product." Notices of the American Mathematical Society 67, no. 07 (August 1, 2020): 1. http://dx.doi.org/10.1090/noti2116.

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28

Akyel, Tuğba, and Tahir Azeroğlu. "Note on the uniqueness holomorphic function on the unit disk." Filomat 32, no. 6 (2018): 2321–25. http://dx.doi.org/10.2298/fil1806321a.

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Let f be an holomorphic function the unit disk to itself. We provide conditions on the local behavior of f along boundary near a finite set of the boundary points that requires f to be a finite Blaschke product.

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29

Sun, Shunhua, Dechao Zheng, and Changyong Zhong. "Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk." Canadian Journal of Mathematics 62, no. 2 (April 1, 2010): 415–38. http://dx.doi.org/10.4153/cjm-2010-026-4.

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AbstractIn this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.

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30

Protas, David. "Mean growth of the derivative of a Blaschke product." Kodai Mathematical Journal 27, no. 3 (October 2004): 354–59. http://dx.doi.org/10.2996/kmj/1104247356.

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31

Bishop, C. J. "An indestructible Blaschke product in the little Bloch space." Publicacions Matemàtiques 37 (January 1, 1993): 95–109. http://dx.doi.org/10.5565/publmat_37193_08.

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32

Glader, Christer, and Mikael Lindström. "Finite Blaschke product interpolation on the closed unit disc." Journal of Mathematical Analysis and Applications 273, no. 2 (September 2002): 417–27. http://dx.doi.org/10.1016/s0022-247x(02)00249-4.

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33

Wegert, Elias, and Ilya Spitkovsky. "On partial isometries with circular numerical range." Concrete Operators 8, no. 1 (January 1, 2021): 176–86. http://dx.doi.org/10.1515/conop-2020-0121.

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Abstract In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂ n cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n. The proof is based on the unitary similarity of A to a compressed shift operator SB generated by a finite Blaschke product B. We then use the description of the numerical range of SB as intersection of Poncelet polygons, a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenter of the vertices of Poncelet polygons involving elliptic functions.

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34

Nakazi, Takahiko. "Intersection of Two Invariant Subspaces." Canadian Mathematical Bulletin 30, no. 2 (June 1, 1987): 129–33. http://dx.doi.org/10.4153/cmb-1987-019-6.

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AbstractIt is shown that, if F and G are inner functions, (H2 ⊖ FH2)/(H2 ⊖ FH2) ∩ GH2 is n-dimensional if and only if G is a Blaschke product of degree n. This is an extension of the well known result for the case (H2 ⊖ FH2) ∩ GH2 = {0}.

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35

Protas, David. "Derivatives of Blaschke Products and Model Space Functions." Canadian Mathematical Bulletin 63, no. 4 (November 12, 2019): 716–25. http://dx.doi.org/10.4153/s0008439519000675.

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Анотація:

AbstractThe relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\unicode[STIX]{x1D6FC}}^{p}$ of the derivative of $B$ or the derivative of functions in its model space $H^{2}\ominus \mathit{BH}^{2}$ is investigated.

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36

Takahashi, Katsutoshi. "On Quasisimilarity for Analytic Toeplitz Operators." Canadian Mathematical Bulletin 31, no. 1 (March 1, 1988): 111–16. http://dx.doi.org/10.4153/cmb-1988-017-7.

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AbstractLet f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf.

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37

Hristov, Miroslav. "Classes and Boundary Properties of Functions in the Open Unit Disk." Proceedings of the Bulgarian Academy of Sciences 75, no. 9 (September 30, 2022): 1255–61. http://dx.doi.org/10.7546/crabs.2022.09.01.

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Let $\psi$ be a Blaschke product and $d\theta(\mathop{\rm supp}\psi)=0$. In this paper we prove that the functions of Bourgain algebra $ (\psi H^\infty (D), L^\infty (D))_b $ have essential non-tangential limit at almost every point of $T=\{z:\mid z\mid = 1\}$.

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38

Cassier, G., and I. Chalendar. "The group of the invariants of a finite blaschke product." Complex Variables, Theory and Application: An International Journal 42, no. 3 (September 2000): 193–206. http://dx.doi.org/10.1080/17476930008815283.

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39

Videnskii, I. V. "Blaschke Product for a Hilbert Space with Schwarz–Pick Kernel." Journal of Mathematical Sciences 215, no. 5 (April 30, 2016): 585–94. http://dx.doi.org/10.1007/s10958-016-2864-4.

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40

Jevtić, Miroljub. "A Note on Blaschke Products with Zeroes in a Nontangential Region." Canadian Mathematical Bulletin 32, no. 1 (March 1, 1989): 18–23. http://dx.doi.org/10.4153/cmb-1989-003-4.

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AbstractWe show that if B is α Blaschke product with nontangential zero set {zk} and 0 < p < 1, 1/2 < αp < 1, then the condition sup0<r<1(l — r) Mp(r, D1+αB) < ∞ is equivalent to the condition {(1 - |zk|(1/p)-αKα} ∊ l∞.

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41

Örnek, Bülent, and Tuğba Akyel. "Representation with majorant of the Schwarz lemma at the boundary." Publications de l'Institut Math?matique (Belgrade) 101, no. 115 (2017): 191–96. http://dx.doi.org/10.2298/pim1715191o.

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Анотація:

Let f be a holomorphic function in the unit disc and |f(z)?1| < 1 for |z| < 1. We generalize the uniqueness portion of Schwarz?s lemma and provide sufficient conditions on the local behavior of f near a finite set of boundary points that needed for f to be a finite Blaschke product.

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42

MASHREGHI, JAVAD, and MAHMOOD SHABANKHAH. "COMPOSITION OPERATORS ON FINITE RANK MODEL SUBSPACES." Glasgow Mathematical Journal 55, no. 1 (August 2, 2012): 69–83. http://dx.doi.org/10.1017/s0017089512000341.

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AbstractWe give a complete description of bounded composition operators on model subspaces KB, where B is a finite Blaschke product. In particular, if B has at least one finite pole, we show that the collection of all bounded composition operators on KB has a group structure. Moreover, if B has at least two distinct finite poles, this group is finite and cyclic.

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43

Bomash, Gregory. "A Blaschke-type product and random zero sets for Bergman spaces." Arkiv för Matematik 30, no. 1-2 (December 1992): 45–60. http://dx.doi.org/10.1007/bf02384861.

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44

Wang, ZongYao, RuiFang Zhao, and YongFei Jin. "Finite Blaschke product and the multiplication operators on Sobolev disk algebra." Science in China Series A: Mathematics 52, no. 1 (August 30, 2008): 142–46. http://dx.doi.org/10.1007/s11425-008-0051-x.

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45

Scheinberg, Stephen. "How Fast Can a Blaschke Product Tend to Zero, and Where?" Computational Methods and Function Theory 13, no. 3 (September 11, 2013): 459–77. http://dx.doi.org/10.1007/s40315-013-0031-1.

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46

Bshouty, D., and W. Hengartner. "Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations." Canadian Journal of Mathematics 51, no. 3 (June 1, 1999): 470–87. http://dx.doi.org/10.4153/cjm-1999-021-8.

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AbstractIn this article we characterize the univalent harmonic mappings from the exterior of the unit disk, Δ, onto a simply connected domain Ω containing infinity and which are solutions of the system of elliptic partial differential equations where the second dilatation function a(z) is a finite Blaschke product. At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice.

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47

Reijonen, Atte. "Necessary and Sufficient Conditions for Inner Functions to Be inQK(p,p-2)-Spaces." Journal of Function Spaces 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/376089.

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Under some regularity conditions onK, inner functions inQK(p,p-2)-spaces are characterized in the following way: an inner function belongs toQK(p,p-2)if and only if it is a Blaschke product associated with{zn}satisfyingsupa∈D∑nK(1-|φa(zn)|)<∞, whereφa(z)=(a-z)/(1-a¯z). The result generalizes earlier theorems in (Essén et al., 2006) and (Pérez-González and Rättyä, 2009).

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48

FUJIMOTO, YOSHIHISA. "HERMAN RINGS OF BLASCHKE PRODUCTS OF DEGREE 3." International Journal of Bifurcation and Chaos 19, no. 01 (January 2009): 445–51. http://dx.doi.org/10.1142/s0218127409023007.

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Let Fa,λbe the Blaschke product of the form Fa,λ= λz2((z - a)/(1 - āz)) and α denote an irrational number satisfying the Brjuno condition. Henriksen [1997] showed that for any α there exists a constant a0≧ 3 and a continuous function λ(a) such that Fa,λ(a)possesses an Herman ring and also that modulus M(a) of the Herman ring approaches 0 as a approaches a0. It is remarked that the question whether a0= 3 holds or not is open. According to the idea of Fagella and Geyer [2003] we can show that for a certain set of irrational rotation numbers, a0is strictly larger than 3.

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49

Du, Juntao, Songxiao Li, and Yecheng Shi. "Weighted composition operators on weighted Bergman spaces induced by doubling weights." MATHEMATICA SCANDINAVICA 126, no. 3 (September 3, 2020): 519–39. http://dx.doi.org/10.7146/math.scand.a-119741.

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In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.

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50

Kucerovsky, Dan, and Aydin Sarraf. "Solving Riemann-Hilbert problems with meromorphic functions." Acta Universitatis Sapientiae, Mathematica 11, no. 1 (August 1, 2019): 117–30. http://dx.doi.org/10.2478/ausm-2019-0010.

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Abstract In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.

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