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Journal articles on the topic 'Functions of several complex variables'

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Published: 4 June 2021
Last updated: 30 July 2024

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1

Liu, Xiang Yang. "Bloch functions of several complex variables." Pacific Journal of Mathematics 152, no. 2 (February 1, 1992): 347–63. http://dx.doi.org/10.2140/pjm.1992.152.347.

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2

Hedenmalm, Håkan. "Outer functions of several complex variables." Journal of Functional Analysis 80, no. 1 (September 1988): 9–15. http://dx.doi.org/10.1016/0022-1236(88)90061-4.

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3

Zhu, Ting, Sheng ao Zhou, and Liu Yang. "On normal functions in several complex variables." Journal of Classical Analysis, no. 1 (2020): 45–58. http://dx.doi.org/10.7153/jca-2020-16-06.

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4

Backlund, Ulf, Linus Carlsson, Anders Fällström, and Håkan Persson. "Semi-Bloch Functions in Several Complex Variables." Journal of Geometric Analysis 26, no. 1 (January 15, 2015): 463–73. http://dx.doi.org/10.1007/s12220-015-9558-x.

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5

ALMIRA, J. M., and KH F. ABU-HELAIEL. "On Montel’s theorem in several variables." Carpathian Journal of Mathematics 31, no. 1 (2015): 1–10. http://dx.doi.org/10.37193/cjm.2015.01.01.

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Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and complex functions of several complex variables.
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6

Sam, Vansak, and Kamthorn Chailuek. "Hardy's Inequality for Functions of Several Complex Variables." Sains Malaysiana 46, no. 9 (September 30, 2017): 1355–59. http://dx.doi.org/10.17576/jsm-2017-4609-01.

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7

Bavrin, I. I. "Integral representations of functions of several complex variables." Doklady Mathematics 75, no. 3 (June 2007): 395–98. http://dx.doi.org/10.1134/s1064562407030179.

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8

Mirotin, A. R. "Properties of Bernstein functions of several complex variables." Mathematical Notes 93, no. 1-2 (January 2013): 257–65. http://dx.doi.org/10.1134/s0001434613010288.

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9

HU, PEI-CHU, and CHUNG-CHUN YANG. "THE TUMURA–CLUNIE THEOREM IN SEVERAL COMPLEX VARIABLES." Bulletin of the Australian Mathematical Society 90, no. 3 (June 13, 2014): 444–56. http://dx.doi.org/10.1017/s0004972714000446.

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AbstractIt is a well-known result that if a nonconstant meromorphic function $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}f$ on $\mathbb{C}$ and its $l$th derivative $f^{(l)}$ have no zeros for some $l\geq 2$, then $f$ is of the form $f(z)=\exp (Az+B)$ or $f(z)=(Az+B)^{-n}$ for some constants $A$, $B$. We extend this result to meromorphic functions of several variables, by first extending the classic Tumura–Clunie theorem for meromorphic functions of one complex variable to that of meromorphic functions of several complex variables using Nevanlinna theory.
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10

Grantcharov, Gueo, and Camilo Montoya. "On Functions of Several Split-Quaternionic Variables." Advances in Mathematical Physics 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/3654530.

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Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a specific complex volume form. In this note we show that similar relation holds for functions of several split-quaternionic variables and point to some relations with geometry.
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11

Shubladze, M. "Hyperplane Singularities of Analytic Functions of Several Complex Variables." gmj 4, no. 2 (April 1997): 163–84. http://dx.doi.org/10.1515/gmj.1997.163.

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Abstract A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.
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12

Lee Stout, E. "Removable sets for holomorphic functions of several complex variables." Publicacions Matemàtiques 33 (July 1, 1989): 345–62. http://dx.doi.org/10.5565/publmat_33289_11.

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13

Qiao, Yuying, Yanyan Cui, Zunfeng Li, and Liping Wang. "k-holomorphic functions in spaces of several complex variables." Complex Variables and Elliptic Equations 65, no. 11 (October 28, 2019): 1826–45. http://dx.doi.org/10.1080/17476933.2019.1681417.

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14

Zehua, Zhou. "The properties of meromorphic functions of several complex variables." Wuhan University Journal of Natural Sciences 3, no. 3 (September 1998): 261–64. http://dx.doi.org/10.1007/bf02829971.

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15

Dovbush, P. V. "Boundary behavior of holomorphic functions of several complex variables." Mathematical Notes of the Academy of Sciences of the USSR 39, no. 3 (March 1986): 196–99. http://dx.doi.org/10.1007/bf01170247.

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16

Dovbush, P. V. "Polynomiality criterion for entire functions of several complex variables." Mathematical Notes 66, no. 4 (October 1999): 409–10. http://dx.doi.org/10.1007/bf02679088.

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17

Perotti, A. "Dirichlet problem for pluriharmonic functions of several complex variables." Communications in Partial Differential Equations 24, no. 3-4 (January 1999): 707–17. http://dx.doi.org/10.1080/03605309908821439.

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18

Aron, Richard M., Javier Falcó, Domingo García, and Manuel Maestre. "Algebras of symmetric holomorphic functions of several complex variables." Revista Matemática Complutense 31, no. 3 (March 17, 2018): 651–72. http://dx.doi.org/10.1007/s13163-018-0261-x.

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19

Gorkin, Pamela, Fernando León-Saavedra, and Raymond Mortini. "Bounded universal functions in one and several complex variables." Mathematische Zeitschrift 258, no. 4 (May 31, 2007): 745–62. http://dx.doi.org/10.1007/s00209-007-0195-3.

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20

Karapetyan, Arman H. "Weighted integral representations of entire functions of several complex variables." Bulletin of the Belgian Mathematical Society - Simon Stevin 15, no. 2 (May 2008): 287–302. http://dx.doi.org/10.36045/bbms/1210254826.

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21

JIN, LU. "A UNICITY THEOREM FOR ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES." Chinese Annals of Mathematics 25, no. 04 (October 2004): 483–92. http://dx.doi.org/10.1142/s0252959904000433.

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22

Bayart, Frédéric, and Paul M. Gauthier. "Functions Universal for all Translation Operators in Several Complex Variables." Canadian Mathematical Bulletin 60, no. 3 (September 1, 2017): 462–69. http://dx.doi.org/10.4153/cmb-2016-069-4.

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23

Abi-Khuzam, Faruk, Florian Bertrand, and Giuseppe Della Sala. "The star function for meromorphic functions of several complex variables." Complex Variables and Elliptic Equations 64, no. 1 (December 10, 2017): 26–39. http://dx.doi.org/10.1080/17476933.2017.1410797.

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24

Klimek, M. "LECTURES ON THE THEORY OF FUNCTIONS OF SEVERAL COMPLEX VARIABLES." Bulletin of the London Mathematical Society 17, no. 5 (September 1985): 503–4. http://dx.doi.org/10.1112/blms/17.5.503.

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25

Alpay, D., and C. Dubi. "A realization theorem for rational functions of several complex variables." Systems & Control Letters 49, no. 3 (July 2003): 225–29. http://dx.doi.org/10.1016/s0167-6911(02)00326-2.

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26

Dovbush, P. V. "Admissible limits of normal holomorphic functions of several complex variables." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 5 (May 1990): 449–53. http://dx.doi.org/10.1007/bf01158086.

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27

Dovbush, P. V. "Existence of admissible limits of functions of several complex variables." Siberian Mathematical Journal 28, no. 3 (1988): 411–14. http://dx.doi.org/10.1007/bf00969572.

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28

Riihentaus, Juhani. "A Removability Result for Holomorphic Functions of Several Complex Variables." Journal of Basic & Applied Sciences 12 (February 3, 2016): 50–52. http://dx.doi.org/10.6000/1927-5129.2016.12.07.

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29

Lin, Qun, and J. G. Rokne. "Circular centered forms for rational functions in several complex variables." Journal of Computational and Applied Mathematics 41, no. 3 (August 1992): 347–57. http://dx.doi.org/10.1016/0377-0427(92)90141-j.

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30

Lu, Jin. "Theorems of Picard type for entire functions of several complex variables." Kodai Mathematical Journal 26, no. 2 (June 2003): 221–29. http://dx.doi.org/10.2996/kmj/1061901063.

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31

Arai, Hitoshi. "Kähler diffusions, carleson measures and BMOA functions of several complex variables." Complex Variables, Theory and Application: An International Journal 22, no. 3-4 (September 1993): 255–66. http://dx.doi.org/10.1080/17476939308814666.

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32

Diederich, Klas. "Book Review: Holomorphic functions and integral representations in several complex variables." Bulletin of the American Mathematical Society 20, no. 1 (January 1, 1989): 132–40. http://dx.doi.org/10.1090/s0273-0979-1989-15730-3.

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33

Dutta, Ratan Kumar, and Nintu Mandal. "Relative p-th Order of Entire Functions of Several Complex Variables." International Journal of Mathematics Trends and Technology 46, no. 4 (June 25, 2017): 235–41. http://dx.doi.org/10.14445/22315373/ijmtt-v46p534.

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34

Adams, W. W., C. A. Berenstein, P. Loustaunau, I. Sabadini, and D. C. Struppa. "Regular functions of several quaternionic variables and the Cauchy-Fueter complex." Journal of Geometric Analysis 9, no. 1 (March 1999): 1–15. http://dx.doi.org/10.1007/bf02923085.

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35

Ivanov, P. A., and S. N. Melikhov. "Pommiez Operator in Spaces of Analytic Functions of Several Complex Variables." Journal of Mathematical Sciences 252, no. 3 (January 2021): 345–59. http://dx.doi.org/10.1007/s10958-020-05164-7.

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36

Hu, Pei-chu, and Chung-chun Yang. "The second main theorem for algebroid functions of several complex variables." Mathematische Zeitschrift 220, no. 1 (December 1995): 99–126. http://dx.doi.org/10.1007/bf02572605.

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37

Einstein-Matthews, S. M., and H. S. Kasana. "Proximate order and type of entire functions of several complex variables." Israel Journal of Mathematics 92, no. 1-3 (February 1995): 273–84. http://dx.doi.org/10.1007/bf02762082.

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38

PETERZIL, YA'ACOV, and SERGEI STARCHENKO. "EXPANSIONS OF ALGEBRAICALLY CLOSED FIELDS II: FUNCTIONS OF SEVERAL VARIABLES." Journal of Mathematical Logic 03, no. 01 (May 2003): 1–35. http://dx.doi.org/10.1142/s0219061303000224.

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Let ℛ be an o-minimal expansion of a real closed field R. We continue here the investigation we began in [11] of differentiability with respect to the algebraically closed field [Formula: see text]. We develop the basic theory of such K-differentiability for definable functions of several variables, proving theorems on removable singularities as well as analogues of the Weierstrass preparation and division theorems for definable functions. We consider also definably meromorphic functions and prove that every definable function which is meromorphic on Kn is necessarily a rational function. We finally discuss definable analogues of complex analytic manifolds, with possible connections to the model theoretic work on compact complex manifolds, and present two examples of "nonstandard manifolds" in our setting.
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39

Trybucka, Edyta. "Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables." Symmetry 11, no. 10 (October 16, 2019): 1304. http://dx.doi.org/10.3390/sym11101304.

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Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular domain of the space C n . We investigate relations between this family and some of type of Bavrin’s families. We give estimates of G-balance of k-homogeneous polynomial, a distortion type theorem and a sufficient condition for functions belonging to this family. Furthermore, we present some examples of functions from the considered class.
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40

Zhou, Xiang Yu. "Recent progress in the theory of functions of several complex variables and complex geometry." Teoreticheskaya i Matematicheskaya Fizika 218, no. 1 (January 2024): 187–203. http://dx.doi.org/10.4213/tmf10554.

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Дан обзор недавних новых результатов в области обратных теорем о $L^2$-существовании и $L^2$-продолжении, составляющих две основные части $L^2$-теории. Эти результаты используются для получения критерия положительности по Гриффитсу и условий положительности по Накано для (сингулярных) эрмитовых метрик голоморфных векторных расслоений, а также для доказательства сильной открытости и устойчивости пучков мультипликативных подмодулей, связанных с сингулярными неотрицательными по Накано эрмитовыми метриками на голоморфных векторных расслоениях.
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41

Zhou, Xiangyu. "Recent progress in the theory of functions of several complex variables and complex geometry." Theoretical and Mathematical Physics 218, no. 1 (January 2024): 163–76. http://dx.doi.org/10.1134/s0040577924010112.

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42

Gaboury, Sébastien, and Richard Tremblay. "An Expansion Theorem Involving H-Function of Several Complex Variables." International Journal of Analysis 2013 (January 30, 2013): 1–6. http://dx.doi.org/10.1155/2013/353547.

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The aim of this present paper is to obtain a general expansion theorem involving H-functions of several complex variables. This is done by making use of a Taylor-like expansion in terms of a rational function obtained by means of fractional derivatives given recently by the authors. Special cases are also computed.
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43

Yang, Liu. "Extensions of p-Yosida functions to holomorphic mappings of several complex variables." Complex Variables and Elliptic Equations 65, no. 10 (October 20, 2019): 1661–71. http://dx.doi.org/10.1080/17476933.2019.1679795.

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44

Długosz, Renata, and Piotr Liczberski. "An application of hypergeometric functions to a construction in several complex variables." Journal d'Analyse Mathématique 137, no. 2 (March 2019): 707–21. http://dx.doi.org/10.1007/s11854-019-0012-z.

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45

Srivastava, G. S., and Susheel Kumar. "On approximation and generalized type of analytic functions of several complex variables." Analysis in Theory and Applications 27, no. 2 (June 2011): 101–8. http://dx.doi.org/10.1007/s10496-011-0101-z.

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46

Cao, T. B., and R. J. Korhonen. "Value distribution of q-differences of meromorphic functions in several complex variables." Analysis Mathematica 46, no. 4 (November 18, 2020): 699–736. http://dx.doi.org/10.1007/s10476-020-0058-2.

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47

Wang, Ermin, and Jiajia Xu. "Toeplitz operators between large Fock spaces in several complex variables." AIMS Mathematics 7, no. 1 (2021): 1293–306. http://dx.doi.org/10.3934/math.2022076.

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<abstract><p>Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Borel measure $ \mu $ on $ {\mathbb C}^n $, we characterize the boundedness and compactness of Toeplitz operator $ T_\mu $ between two large Fock spaces $ F^{p}_\omega $ and $ F^{q}_\omega $ for all possible $ 0 &lt; p, q &lt; \infty $.</p></abstract>
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48

Zhou, Jun, and Zhaoxia Duan. "Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables." Mathematical Problems in Engineering 2019 (August 6, 2019): 1–10. http://dx.doi.org/10.1155/2019/7971495.

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The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in n-variable complex functions is carried out one-by-one in terms of each and all variables, namely, partially, so that argument-principle-like relations are established in poly-disc neighborhoods of the variable domains, namely locally. The technique is applicable graphically with loci plotting, independent of Cauchy integral contour and locus orientations; it is also numerically tractable without loci plotting via argument incremental integration. Numerical examples are included to illustrate the main results.
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49

Iida, Yasuo. "Topological properties of the Fréchet space of holomorphic functions of several complex variables." Mathematica Montisnigri 58 (2023): 5–16. http://dx.doi.org/10.20948/mathmontis-2023-58-1.

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Let 𝑁p(𝐵n) (𝑝 > 1) be the Privalov class of holomorphic functions on the unit ball 𝐵n in the space of 𝑛-complex variables. The class 𝑁p(𝐵n) (𝑝 > 1), equipped with the topology given by a natural metric, becomes an 𝐹-algebra. In this paper, we shall introduce a Fréchet space Fp(𝐵n) (𝑝 > 1) of holomorphic functions on 𝐵n which contains 𝑁p(𝐵n). Moreover, we shall characterize some topological properties of Fp(𝐵n) induced by the family of semi norms on Fp(𝐵n) .
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50

Nishimura, Yasuichiro. "Entire functions of several complex variables bounded outside a set of finite volume." Publications of the Research Institute for Mathematical Sciences 23, no. 3 (1987): 487–99. http://dx.doi.org/10.2977/prims/1195176442.

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