Journal articles: 'Meromorphic extension'

1

Hai, L., N. Khue, and N. Nga. "Weak meromorphic extension." Colloquium Mathematicum 64, no. 1 (1993): 65–70. http://dx.doi.org/10.4064/cm-64-1-65-70.

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2

Le Mau Hai and Nguyen Van Khue. "Meromorphic extension spaces." Annales de l’institut Fourier 42, no. 3 (1992): 501–15. http://dx.doi.org/10.5802/aif.1300.

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3

Merker, Joël, and Egmont Porten. "On the local meromorphic extension of CR meromorphic mappings." Annales Polonici Mathematici 70 (1998): 163–93. http://dx.doi.org/10.4064/ap-70-1-163-193.

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4

SARKIS, FRÉDÉRIC. "CR-MEROMORPHIC EXTENSION AND THE NONEMBEDDABILITY OF THE ANDREOTTI–ROSSI CR STRUCTURE IN THE PROJECTIVE SPACE." International Journal of Mathematics 10, no. 07 (November 1999): 897–915. http://dx.doi.org/10.1142/s0129167x99000380.

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Let [Formula: see text] be a polynomially convex compact set and let M be a (2p-1) dimensional (p ≥ 2) maximally complex bounded scarred C1 submanifold of [Formula: see text], irreducible in the current sense. According to Harvey–Lawson [14] and Chirka [4], there exists a bounded irreducible analytic set [Formula: see text] such that [M]=±d[T]. In this paper, we prove that every CR-meromorphic map carrying M into a projective manifold V extends to a meromorphic map F:T → V. We extend the notion of CR-meromorphic maps to CR submanifolds of [Formula: see text] and give another proof of our extension theorem which extends to the greater codimensional case. We also apply our extension result to prove a Lewy type extension theorem for CR-meromorphic maps, a Hartogs type theorem in [Formula: see text] and the non embedding of the Andreotti–Rossi CR structure in [Formula: see text].

5

Mol, Rogério S. "Meromorphic first integrals: some extension results." Tohoku Mathematical Journal 54, no. 1 (March 2002): 85–104. http://dx.doi.org/10.2748/tmj/1113247181.

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6

Chiappari, Stephen A. "Holomorphic extension of proper meromorphic mappings." Michigan Mathematical Journal 38, no. 2 (1991): 167–74. http://dx.doi.org/10.1307/mmj/1029004326.

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7

Nordin, Azmeer, and Mohd Salmi Md Noorani. "Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts." Mathematics 9, no. 11 (June 1, 2021): 1268. http://dx.doi.org/10.3390/math9111268.

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For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the system. Specifically, the existence of a non-vanishing meromorphic extension of the zeta function leads to certain asymptotic results. In this paper, we prove the asymptotic behaviours of the counting functions for a certain type of shift spaces induced by directed bouquet graphs and Dyck shifts. We call these shift spaces as the bouquet-Dyck shifts. Since their respective zeta function involves square roots of polynomials, the meromorphic extension is difficult to be obtained. To overcome this obstacle, we employ some theories on zeros of polynomials, including the well-known Eneström–Kakeya Theorem in complex analysis. Finally, the meromorphic extension will imply the desired asymptotic results.

8

Domrin, Andrei V. "Meromorphic extension of solutions of soliton equations." Izvestiya: Mathematics 74, no. 3 (June 23, 2010): 461–80. http://dx.doi.org/10.1070/im2010v074n03abeh002494.

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9

Zheng, Jian-Hua. "A Quantitative Estimate on Fixed-Points of Composite Meromorphic Functions." Canadian Mathematical Bulletin 38, no. 4 (December 1, 1995): 490–95. http://dx.doi.org/10.4153/cmb-1995-071-x.

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AbstractLet ƒ(z) be a transcendental meromorphic function of finite order, g(z) a transcendental entire function of finite lower order and let α(z) be a non-constant meromorphic function with T(r, α) = S(r,g). As an extension of the main result of [7], we prove thatwhere J has a positive lower logarithmic density.

10

Xu, Hong Yan, and Xiu Min Zheng. "The properties of solutions for several types of Painlevé equations concerning fixed-points, zeros and poles." Open Mathematics 17, no. 1 (August 28, 2019): 1014–24. http://dx.doi.org/10.1515/math-2019-0079.

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Abstract The purpose of this manuscript is to study some properties on meromorphic solutions for several types of q-difference equations. Some exponents of convergence of zeros, poles and fixed points related to meromorphic solutions for some q-difference equations are obtained. Our theorems are some extension and improvements to those results given by Qi, Peng, Chen, and Zhang.

11

Živković-Zlatanović, S. Č., and B. P. Duggal. "Generalized Kato-meromorphic decomposition, generalized Drazin-meromorphic invertible operators and single-valued extension property." Banach Journal of Mathematical Analysis 14, no. 3 (January 1, 2020): 894–914. http://dx.doi.org/10.1007/s43037-019-00044-y.

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12

Lahiri, Indrajit. "Generalisation of an inequality of C.T. Chuang to vector meromorphic functions." Bulletin of the Australian Mathematical Society 46, no. 2 (October 1992): 317–33. http://dx.doi.org/10.1017/s000497270001193x.

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13

Jordá, Enrique. "Extension of vector-valued holomorphic and meromorphic functions." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 1 (April 2005): 5–21. http://dx.doi.org/10.36045/bbms/1113318125.

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14

Shirosaki, Manabu. "An extension of unicity theorem for meromorphic functions." Tohoku Mathematical Journal 45, no. 4 (1993): 491–97. http://dx.doi.org/10.2748/tmj/1178225843.

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15

Kazaryan, M. V. "MEROMORPHIC EXTENSION WITH RESPECT TO GROUPS OF VARIABLES." Mathematics of the USSR-Sbornik 53, no. 2 (February 28, 1986): 385–98. http://dx.doi.org/10.1070/sm1986v053n02abeh002927.

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16

Bhowmik, B., G. Satpati, and T. Sugawa. "Quasiconformal extension of meromorphic functions with nonzero pole." Proceedings of the American Mathematical Society 144, no. 6 (October 22, 2015): 2593–601. http://dx.doi.org/10.1090/proc/12933.

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17

Soh, L. L. "Valiron Deficient Functions of Meromorphic Functions: An Extension." Journal of Mathematical Analysis and Applications 188, no. 1 (November 1994): 286–96. http://dx.doi.org/10.1006/jmaa.1994.1428.

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18

Oanh, Bui Thi Kieu, and Ngo Thi Thu Thuy. "Uniqueness of Differential Polynomials of Meromorphic Functions Sharing a Small Function Without Counting Multiplicity." Fasciculi Mathematici 57, no. 1 (December 1, 2016): 121–35. http://dx.doi.org/10.1515/fascmath-2016-0020.

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Abstract The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].

19

Yazici, Ozcan. "Holomorphic extension of meromorphic mappings along real analytic hypersurfaces." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 4 (October 26, 2019): 1337–42. http://dx.doi.org/10.1007/s10231-019-00923-z.

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20

Pekař, L., and R. Prokop. "The revision and extension of the RMS ring for time delay systems." Bulletin of the Polish Academy of Sciences Technical Sciences 65, no. 3 (June 27, 2017): 341–49. http://dx.doi.org/10.1515/bpasts-2017-0038.

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AbstractThis paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.a. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMSsimply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions RQMis established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.

21

KOO, JA KYUNG, DONG HWA SHIN, and DONG SUNG YOON. "NORMAL BASES FOR MODULAR FUNCTION FIELDS." Bulletin of the Australian Mathematical Society 95, no. 3 (March 2, 2017): 384–92. http://dx.doi.org/10.1017/s0004972716001362.

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We provide a concrete example of a normal basis for a finite Galois extension which is not abelian. More precisely, let $\mathbb{C}(X(N))$ be the field of meromorphic functions on the modular curve $X(N)$ of level $N$. We construct a completely free element in the extension $\mathbb{C}(X(N))/\mathbb{C}(X(1))$ by means of Siegel functions.

22

Cimpoeaş, Mircea, and Florin Nicolae. "Independence of Artin L-functions." Forum Mathematicum 31, no. 2 (March 1, 2019): 529–34. http://dx.doi.org/10.1515/forum-2018-0185.

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AbstractLet {K/\mathbb{Q}} be a finite Galois extension. Let {\chi_{1},\ldots,\chi_{r}} be {r\geq 1} distinct characters of the Galois group with the associated Artin L-functions {L(s,\chi_{1}),\ldots,L(s,\chi_{r})}. Let {m\geq 0}. We prove that the derivatives {L^{(k)}(s,\chi_{j})}, {1\leq j\leq r}, {0\leq k\leq m}, are linearly independent over the field of meromorphic functions of order {<1}. From this it follows that the L-functions corresponding to the irreducible characters are algebraically independent over the field of meromorphic functions of order {<1}.

23

Quang, Si Duc. "Extension and normality of meromorphic mappings into complex projective varieties." Annales Polonici Mathematici 104, no. 3 (2012): 279–92. http://dx.doi.org/10.4064/ap104-3-5.

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24

JARNICKI, Marek, and Peter PFLUG. "AN EXTENSION THEOREM FOR SEPARATELY MEROMORPHIC FUNCTIONS WITH PLURIPOLAR SINGULARITIESINEQUALITIES." Kyushu Journal of Mathematics 57, no. 2 (2003): 291–302. http://dx.doi.org/10.2206/kyushujm.57.291.

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25

Haydn, Nicolai T. A. "Meromorphic extension of the zeta function for Axiom A flows." Ergodic Theory and Dynamical Systems 10, no. 2 (June 1990): 347–60. http://dx.doi.org/10.1017/s0143385700005587.

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AbstractWe prove the meromorphicity of the zeta function on shifts of finite type for Hölder continuous functions assuming that the essential spectrum of the associated Ruelle operator is contained in the open unit disc. This result allows to extend the region of meromorphicity of the zeta function for Axiom A flows by a strip whose width is determined by the contraction rate of the flow.

26

Soni, Amit, and Shashi Kant. "A New Subclass of Meromorphic Close-to-Convex Functions." Journal of Complex Analysis 2013 (January 8, 2013): 1–5. http://dx.doi.org/10.1155/2013/629394.

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A new subclass MK(t, A, B) of meromorphic close-to-convex functions, defined by means of subordination, is investigated. Some results such as inclusion relationship, coefficient inequality, convolution property, and distortion property for this class are derived. The results obtained here are extension of earlier known work.

27

Nordin, Azmeer, and Mohd Salmi Md Noorani. "Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function." Mathematics 8, no. 5 (May 1, 2020): 685. http://dx.doi.org/10.3390/math8050685.

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The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift. The proof relies on the meromorphic extension of its Artin–Mazur zeta function.

28

Gonzalez, Ivan, Karen Kohl, Lin Jiu, and Victor H. Moll. "An extension of the method of brackets. Part 1." Open Mathematics 15, no. 1 (September 27, 2017): 1181–211. http://dx.doi.org/10.1515/math-2017-0100.

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Abstract The method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n ∈ ℂ, but might vanish or blow up when n ∈ ℕ. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.

29

Bonilla, A., and J. C. Fariña. "Lip α Approximation on Closed Sets with Lip α Extension." Canadian Mathematical Bulletin 38, no. 1 (March 1, 1995): 23–33. http://dx.doi.org/10.4153/cmb-1995-004-3.

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AbstractLet F be a relatively closed subset of a domain G in the complex plane. Let f be a function that is the limit, in the Lip α norm on F, of functions which are holomorphic or meromorphic on G (0 < α < 1). We prove that, under the same conditions that give Lip α-approximation (0 < α < 1 ) on relatively closed subsets of G, it is possible to choose the approximating function m in such a way that f — m can be extended to a function belonging to lip

30

Pflug, Peter, and Viêt Anh Nguyên. "Extension theorems of Sakai type for separately holomorphic and meromorphic functions." Annales Polonici Mathematici 82, no. 2 (2003): 171–87. http://dx.doi.org/10.4064/ap82-2-7.

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31

Toda, Nobushige. "An extension of the derivative of meromorphic functions to holomorphic curves." Proceedings of the Japan Academy, Series A, Mathematical Sciences 70, no. 6 (1994): 159–63. http://dx.doi.org/10.3792/pjaa.70.159.

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32

Lutterodt, C. H. "A meromorphic extension of oka-weil approximation in a stein manifold." Complex Variables, Theory and Application: An International Journal 16, no. 2-3 (April 1991): 153–62. http://dx.doi.org/10.1080/17476939108814477.

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33

Ivashkovich, S. "An Example Concerning Extension and Separate Analyticity Properties of Meromorphic Mappings." American Journal of Mathematics 121, no. 1 (1999): 97–130. http://dx.doi.org/10.1353/ajm.1999.0005.

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34

Amroun, Abdelhamid. "Meromorphic extension of the zeta function for subshifts on countable sets." Bulletin des Sciences Mathématiques 128, no. 4 (April 2004): 303–13. http://dx.doi.org/10.1016/j.bulsci.2004.02.003.

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35

Runckel, Hans-J. "Meromorphic extension of analytic continued fractions across the line of nonconvergence." Rocky Mountain Journal of Mathematics 21, no. 1 (March 1991): 539–56. http://dx.doi.org/10.1216/rmjm/1181073022.

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36

Steinhurst, Benjamin A., and Alexander Teplyaev. "Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals." Letters in Mathematical Physics 103, no. 12 (August 17, 2013): 1377–88. http://dx.doi.org/10.1007/s11005-013-0649-y.

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37

Totoi, Elisabeta-Alina, and Luminiţa-Ioana Cotîrlă. "Preserving Classes of Meromorphic Functions through Integral Operators." Symmetry 14, no. 8 (July 28, 2022): 1545. http://dx.doi.org/10.3390/sym14081545.

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We consider three new classes of meromorphic functions defined by an extension of the Wanas operator and two integral operators, in order to study some preservation properties of the classes. The purpose of the paper is to find the conditions such that, when we apply the integral operator Jp,γ to some function from the new defined classes ΣSp,qn(α,δ), respectively ΣSp,qn(α), we obtain also a function from the same class. We also define a new integral operator on the class of meromorphic functions, denoted by Jp,γ,h, where h is a normalized analytic function on the unit disc. We study some basic properties of this operator. Then we look for the conditions which allow this operator to preserve a particular subclass of the classes mentioned above.

38

Rocha, André. "Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 1 (January 1996): 179–90. http://dx.doi.org/10.1017/s0305004100074065.

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AbstractWe prove the existence of a piecewise analytic expanding map associated to certain Kleinian groups without parabolics acting in the 3-dimensional hyperbolic space. These groups have a fundamental domain ℛ with the property that the geodesic planes containing each face are part of the tesselation. We use this map together with the methods of thermodynamic formalism to give another proof that the Selberg zeta function for such groups has a meromorphic extension to ℂ.

39

Ghanim, Firas, Khalifa Al-Shaqsi, Maslina Darus, and Hiba Fawzi Al-Janaby. "Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function." Mathematics 9, no. 2 (January 19, 2021): 192. http://dx.doi.org/10.3390/math9020192.

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Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity.

40

Ivashkovich, Sergey. "Extension properties of meromorphic mappings with values in non-Kähler complex manifolds." Annals of Mathematics 160, no. 3 (November 1, 2004): 795–837. http://dx.doi.org/10.4007/annals.2004.160.795.

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41

Korhonen, Risto. "An extension of Picard's theorem for meromorphic functions of small hyper-order." Journal of Mathematical Analysis and Applications 357, no. 1 (September 2009): 244–53. http://dx.doi.org/10.1016/j.jmaa.2009.04.011.

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42

Quang, Thai Thuan, and Lien Vuong Lam. "Levi Extension Theorems for Meromorphic Functions of Weak Type in Infinite Dimension." Complex Analysis and Operator Theory 10, no. 7 (April 13, 2016): 1619–54. http://dx.doi.org/10.1007/s11785-016-0548-1.

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43

Ivashkovich, S. M. "The Hartogs-type extension theorem for meromorphic maps into compact K�hler manifolds." Inventiones Mathematicae 109, no. 1 (December 1992): 47–54. http://dx.doi.org/10.1007/bf01232018.

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44

Mazzeo, Rafe R., and Richard B. Melrose. "Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature." Journal of Functional Analysis 75, no. 2 (December 1987): 260–310. http://dx.doi.org/10.1016/0022-1236(87)90097-8.

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45

Ólafsson, G., and A. Pasquale. "On the Meromorphic Extension of the Spherical Functions on Noncompactly Causal Symmetric Spaces." Journal of Functional Analysis 181, no. 2 (April 2001): 346–401. http://dx.doi.org/10.1006/jfan.2000.3721.

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46

Dinh, Tien-Cuong, and Fr�d�ric Sarkis. "Wedge removability of metrically thin sets and application to the CR-meromorphic extension." Mathematische Zeitschrift 238, no. 3 (November 1, 2001): 639–54. http://dx.doi.org/10.1007/s002090100273.

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47

Angeli, Y. "Meromorphic extension of the spherical functions on a class of ordered symmetric spaces." Journal of Functional Analysis 224, no. 1 (July 2005): 49–71. http://dx.doi.org/10.1016/j.jfa.2004.08.012.

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48

Hassani, Ali. "On the meromorphic continuation of the Mellin transform associated to the wave kernel on Riemannian symmetric spaces of the non-compact type." AIMS Mathematics 9, no. 6 (2024): 14731–46. http://dx.doi.org/10.3934/math.2024716.

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<abstract><p>We considered the Mellin transform assigned to the convolution wave kernel associated to the Laplace-Beltrami operator on higher rank Riemannian symmetric spaces of the non-compact type. The occurrence of the analyticity strip of this transform can be deduced directly from the pointwise kernel estimates. Using the zeta function techniques, we established its meromorphic extension to the entire complex plane $ {{\Bbb C}} $ with simple poles on the real line.</p></abstract>

49

Runckel, Hans-J. "Meromorphic extension of analytic continued fractions across their divergence line with applications to orthogonal polynomials." Transactions of the American Mathematical Society 334, no. 1 (January 1, 1992): 183–212. http://dx.doi.org/10.1090/s0002-9947-1992-1072106-8.

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50

Barlet, Daniel. "Real canonical cycle and asymptotics of oscillating integrals." Nagoya Mathematical Journal 171 (2003): 187–96. http://dx.doi.org/10.1017/s0027763000025563.

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AbstractLet Xℝ ⊂ ℝN a real analytic set such that its complexification Xℂ ⊂ ℂN is normal with an isolated singularity at 0. Let fℝ : Xℝ → ℝ a real analytic function such that its complexification fℂ : Xℂ → ℂ has an isolated singularity at 0 in Xℂ. Assuming an orientation given on to a connected component A of we associate a compact cycle Γ(A) in the Milnor fiber of fℂ which determines completely the poles of the meromorphic extension of or equivalently the asymptotics when T → ±∞ of the oscillating integrals . A topological construction of Γ(A) is given. This completes the results of [BM] paragraph 6.

Journal articles on the topic 'Meromorphic extension'

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