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Relevant bibliographies by topics / Pseudoconvex domains. Functions of several complex variables

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Academic literature on the topic 'Pseudoconvex domains. Functions of several complex variables'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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Journal articles on the topic "Pseudoconvex domains. Functions of several complex variables"

1

Bourchtein, Ludmila, and Andrei Bourchtein. "Logarithmically Convex Reinhardt Domains." Ciência e Natura 25, no. 25 (2003): 07. http://dx.doi.org/10.5902/2179460x27233.

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The domains of certain types, such as Reinhardt ones, are important in different problems of theory of functions of several complex variables. For instance, any power series of several complex variables converges in the complete logarithmically convex Reinhardt domain. In this article we prove the logarithmic convexity of complete convex Reinhardt domain.

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2

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 variab

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3

Bourchtein, Ludmila, and Andrei Bourchtein. "Some properties of Reinhardt and Hartogs domains." Ciência e Natura 24, no. 24 (2002): 07. http://dx.doi.org/10.5902/2179460x27130.

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The domains of certain types, such as Reinhardt and Hartogs, are used in different problems of theory of functions of several complex variables. For instance, any power series of several complex variables converges in the complete logarithmically convex Reinhardt domain. Transformations of Reinhardt and Hartogs allow us to diminish the dimension of space and to consider some type of domains using its images. This allows the visibility of the geometric representation and the simplification of the study of properties of such domains. In this article we consider some properties of Reinhardt and H

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4

Abul-Ez, M., H. Abd-Elmageed, M. Hidan, and M. Abdalla. "On the Growth Order and Growth Type of Entire Functions of Several Complex Matrices." Journal of Function Spaces 2020 (February 17, 2020): 1–9. http://dx.doi.org/10.1155/2020/4027529.

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In this paper, we establish an explicit relation between the growth of the maximum modulus and the Taylor coefficients of entire functions in several complex matrix variables (FSCMVs) in hyperspherical regions. The obtained formulas enable us to compute the growth order and the growth type of some higher dimensional generalizations of the exponential, trigonometric, and some special FSCMVs which are analytic in some extended hyperspherical domains. Furthermore, a result concerning linear substitution of the mode of increase of FSCMVs is given.

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5

Cui, Yanyan, Chaojun Wang, and Sifeng Zhu. "Research on Geometric Mappings in Complex Systems Analysis." Discrete Dynamics in Nature and Society 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4732704.

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We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclus

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6

Dou, Xinyuan, Guangbin Ren, Irene Sabadini, and Ting Yang. "Weak Slice Regular Functions on the n-Dimensional Quadratic Cone of Octonions." Journal of Geometric Analysis 31, no. 11 (2021): 11312–37. http://dx.doi.org/10.1007/s12220-021-00682-5.

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AbstractIn the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called n-dimensional quadratic cone of octonions.

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7

Kumar, Devendra. "Best ${L^p}$-approximation of generalized biaxially symmetric potentials over Carath'eodory domains in ${C^N}$ having slow growth." Tamkang Journal of Mathematics 33, no. 3 (2002): 223–32. http://dx.doi.org/10.5556/j.tkjm.33.2002.223-232.

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Let $ F$ be a real valued generalized biaxially symmetric potentials (GBASP) defined on the Caratheodory domain on $ C^N$. Let $ L_\mu^p(D)$ be the class of all functions $ F$ holomorphic on $ D$ such that $ \parallel F\parallel_{D,p}=[\int_D\mid F\mid^pd\mu]^{1\over p}$. Where $ \mu$ is the positive finite, Boral measure with regular asymptotic distribution on $ C^N$. For $ F\in L_{\mu}^p(D)$, set $ E_n^p(F)=\inf\{\parallel F-P\parallel_{D,p}:P\in H_n\}$, $ H_n$ consist of all real biaxisymmetric harmonic polynomials of degree at most $ 2n$. The paper deals with the growth of entire function

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8

Şimon-Marinică, Adrian Bogdan, Nicolae-Ioan Vlasin, Florin Manea, and Gheorghe-Daniel Florea. "Finite element method to solve engineering problems using ansys." MATEC Web of Conferences 342 (2021): 01015. http://dx.doi.org/10.1051/matecconf/202134201015.

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The Finite Element Analysis method, is a powerful computational technique for approximate solutions to a variety of real – world engineering problems having complex domains subjected to general boundary conditions. The method itself has become an essential step in the design or modelling of a physical phenomenon in various engineering disciplines. A physical phenomenon usually occurs in a continuum of matter (solid, liquid or gas) involving several field variables. The field variables vary from point to point, thus possessing an infinite number of solutions in the domain. The basis of finite v

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9

Coco, Armando, Gilda Currenti, Ciro Del Negro, and Giovanni Russo. "A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology." Communications in Computational Physics 16, no. 4 (2014): 983–1009. http://dx.doi.org/10.4208/cicp.210713.010414a.

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AbstractWe propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains. The technique is based on a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary geometries are defined by suitable level-set functions. The equations are discretized by classical nine-point stencil on interior points, while boundary conditions and high order reconstructions are used to define the field variables at ghost-points, which are grid nodes external to the domain with a

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10

PAULSEN, VERN I., GELU POPESCU, and DINESH SINGH. "ON BOHR'S INEQUALITY." Proceedings of the London Mathematical Society 85, no. 2 (2002): 493–512. http://dx.doi.org/10.1112/s0024611502013692.

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Bohr's inequality says that if $f(z) = \sum^{\infty}_{n = 0} a_n z^n$ is a bounded analytic function on the closed unit disc, then $\sum^{\infty}_{n = 0} \lvert a_n\rvert r^n \leq \Vert f\Vert_{\infty}$ for $0 \leq r \leq 1/3$ and that $1/3$ is sharp. In this paper we give an operator-theoretic proof of Bohr's inequality that is based on von Neumann's inequality. Since our proof is operator-theoretic, our methods extend to several complex variables and to non-commutative situations.We obtain Bohr type inequalities for the algebras of bounded analytic functions and the multiplier algebras of re

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Dissertations / Theses on the topic "Pseudoconvex domains. Functions of several complex variables"

1

Lan, Ma. "Abschätzungen von Lösungen der [delta bar]-Gleichung auf streng q-konvexen Mengen mit nicht glattem Rand." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20436892.html.

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2

Biswas, Chandan. "Analytic Continuation In Several Complex Variables." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2331.

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We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study is radically different from that of domains in C by discussing some examples of special types of domains in Cn , n ≥2, such that every function holomorphic on them extends to strictly larger domains. Given a domain in Cn , n ≥ 2, we wish to construct the maximal domain of existence for the holomorphic functions defined on the given domain. This leads to Thullen’s construction o

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3

McBride, Matthew Scott. "D-bar and Dirac Type Operators on Classical and Quantum Domains." 2012. http://hdl.handle.net/1805/2931.

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Indiana University-Purdue University Indianapolis (IUPUI)<br>I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the inverse or inverse modulo compact operators to these operators are computed. These inverses/parametrices are also shown to be bounded and are also shown to be compact, if possible. Also the index of some of the d-bar operators are computed when it doesn't have trivial index. Finally a certain type of limit statement can be said bet

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Books on the topic "Pseudoconvex domains. Functions of several complex variables"

1

1943-, Pflug Peter, ed. First steps in several complex variables: Reinhardt domains. European Mathematical Society, 2008.

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2

Milnor, John W. Dynamical systems (1984-2012). Edited by Bonifant Araceli 1963-. American Mathematical Society, 2014.

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3

Several complex variables II: Function theory in classical domains : complex potential theory. Springer-Verlag, 1994.

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4

(Contributor), L. A. Aizenberg, A. B. Aleksandrov (Contributor), A. Sadullaev (Contributor), et al., eds. Several Complex Variables II: Function Theory in Classical Domains. Complex Potential Theory (Encyclopaedia of Mathematical Sciences). Springer, 1994.

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5

Passare, Mikael, Ragnar Sigurdsson, and Mats Andersson. Complex Convexity and Analytic Functionals (Progress in Mathematics). Birkhäuser Basel, 2004.

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6

Koranyi, Adam, Soji Kaneyuki, and Jacques Faraut. Analysis and Geometry on Complex Homogeneous Domains. Springer, 2012.

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7

Kaneyuki, Soji, Adam Koranyi, Qi-keng Lu, Guy Roos, and Jacques Faraut. Analysis and Geometry on Complex Homogeneous Domains (Progress in Mathematics). Birkhäuser Boston, 1999.

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Book chapters on the topic "Pseudoconvex domains. Functions of several complex variables"

1

Hirachi, Kengo, and Gen Komatsu. "Local Sobolev—Bergman Kernels of Strictly Pseudoconvex Domains." In Analysis and Geometry in Several Complex Variables. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-2166-1_5.

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2

Ohsawa, Takeo. "Pseudoconvex Domains in ℙ n : A Question on the 1-Convex Boundary Points." In Analysis and Geometry in Several Complex Variables. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-2166-1_11.

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3

Beals, Richard, and Nancy K. Stanton. "The Heat Equation for the % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacq % GHciITaaaaaa!376B! $$\overline \partial$$ -Neumann Problem on Strictly Pseudoconvex Domains." In Contributions to Several Complex Variables. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-06816-7_2.

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4

"Pseudoconvex domains." In Lectures on Counterexamples in Several Complex Variables. American Mathematical Society, 2007. http://dx.doi.org/10.1090/chel/363/06.

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5

"Pseudoconvex domains without pseudoconvex exhaustion." In Lectures on Counterexamples in Several Complex Variables. American Mathematical Society, 2007. http://dx.doi.org/10.1090/chel/363/13.

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6

"Integral Formulas for Strictly Pseudoconvex Domains." In Several Complex Variables and Integral Formulas. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708236_0003.

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7

"The $\overline{\partial}$ Problem in Pseudoconvex Domains." In Several Complex Variables and Integral Formulas. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708236_0002.

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8

"𝐿² theory for \overline∂ on pseudoconvex domains." In Partial Differential Equations in Several Complex Variables. American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/019/04.

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9

"Boundary regularity for \overline∂ on pseudoconvex domains." In Partial Differential Equations in Several Complex Variables. American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/019/06.

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10

"Chapter III. Potential theory for strictly pseudo-convex domains." In Boundary Behavior of Holomorphic Functions of Several Complex Variables. (MN-11). Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400871261-006.

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Conference papers on the topic "Pseudoconvex domains. Functions of several complex variables"

1

Daxberger, Erik, Anastasia Makarova, Matteo Turchetta, and Andreas Krause. "Mixed-Variable Bayesian Optimization." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/365.

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The optimization of expensive to evaluate, black-box, mixed-variable functions, i.e. functions that have continuous and discrete inputs, is a difficult and yet pervasive problem in science and engineering. In Bayesian optimization (BO), special cases of this problem that consider fully continuous or fully discrete domains have been widely studied. However, few methods exist for mixed-variable domains and none of them can handle discrete constraints that arise in many real-world applications. In this paper, we introduce MiVaBo, a novel BO algorithm for the efficient optimization of mixed-variab

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