Search Results - "Polynomials and rational functions of one complex variable"

Inequalities of Turán Type for the Polar Derivative of a Polynomial: Inequalities of Turán type for the polar derivative of a polynomial

Authors: Mir, A. Bhat, A. H. Thoker, W. A.

Source: Siberian Mathematical Journal. 66:168-176

Subject Terms: polar derivative, polynomials, Polynomials and rational functions of one complex variable, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), zeros, Inequalities in the complex plane, Turán inequality

File Description: application/xml

Access URL: https://zbmath.org/7982523
https://doi.org/10.1134/s0037446625010136

Extension of Turán-type inequalities for polar derivatives of polynomials into integral mean version

Authors: Chanam, Barchand

Source: Publications de l'Institut Mathematique. 116:75-85

Subject Terms: polar derivative, polynomials, Polynomials and rational functions of one complex variable, Turán type inequalities, Special classes of entire functions of one complex variable and growth estimates, Inequalities in the complex plane, \(L^r\)-norm inequalities

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Schinzel-type bounds for the Mahler measure on lemniscates

Authors: Looney, Ryan Pritsker, Igor

Source: Mathematics of Computation.

Subject Terms: PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Polynomials and rational functions of one complex variable, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Polynomials in real and complex fields: location of zeros (algebraic theorems), lemniscates, 0101 mathematics, Discrete potential theory, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7962058
https://doi.org/10.1090/mcom/3985

Some Lp norm involving the polar derivative of a polynomial: Some \(L_p\) norm involving the polar derivative of a polynomial

Authors: Irfan Ahmad Wani Mohammad Ibrahim Mir Ishfaq Nazir

Source: Asian-European Journal of Mathematics. 17

Subject Terms: polynomials, inequalities, Polynomials and rational functions of one complex variable, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), derivative and polar derivative, zeros, Inequalities in the complex plane, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7956150
https://doi.org/10.1142/s1793557124500372

Bemerkungen über Iterierten von Polynomen: Bemerkungen über Iterierte von Polynomen

Authors: Fehér, János

Source: Publicationes Mathematicae Debrecen. 31:1-5

Subject Terms: fixed point, Polynomials and rational functions of one complex variable, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3879219

Typically real polynomials

Authors: Royster, Wimberley Calvin Suffridge, Teddy J. Uniwersytet Marii Curie-Skłodowskiej (Lublin)

Contributors: Royster, Wimberley Calvin Suffridge, Teddy J. Uniwersytet Marii Curie-Skłodowskiej (Lublin)

Source: Publicationes Mathematicae Debrecen. 17:307-312

Subject Terms: Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Coefficient problems for univalent and multivalent functions of one complex variable, Polynomials and rational functions of one complex variable, 0103 physical sciences, matematyka, Conformal mappings of special domains, 01 natural sciences

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/3386021
https://zbmath.org/3372360

On effectiveness of basic sets of polynomials associated with functions of algebraic infinite matrices

Authors: Makar, Ragy H. Fawzy, Laila

Source: Publicationes Mathematicae Debrecen. 25:73-76

Subject Terms: Polynomials and rational functions of one complex variable, Dirichlet series, exponential series and other series in one complex variable, Functions of Algebraic Infinite Matrices, 0101 mathematics, Polynomials, 01 natural sciences

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Access URL: https://zbmath.org/3608374

On the number of components of random polynomial lemniscates

Authors: Ghosh, Subhajit

Source: Electronic Journal of Probability. 29

Subject Terms: Random power series in one complex variable, polynomials, Mathematics - Complex Variables, 60D05, 30C15, Probability (math.PR), random lemniscates, Mathematics - Classical Analysis and ODEs, Polynomials and rational functions of one complex variable, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Classical Analysis and ODEs (math.CA), FOS: Mathematics, Geometric probability and stochastic geometry, Complex Variables (math.CV), Mathematics - Probability

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Access URL: http://arxiv.org/abs/2306.10795

A proof of A. Gabrielov’s rank theorem: A proof of A. Gabrielov's rank theorem

Authors: Belotto da Silva, André Curmi, Octave Rond, Guillaume

Contributors: Belotto da Silva, André Curmi, Octave Rond, Guillaume

Source: Journal de l’École polytechnique — Mathématiques. 8:1329-1396

Subject Terms: Primary 13J05, 32B05, Secondary 12J10, 13A18, 13B35, 14B05, 14B20, 30C10, 32A22, 32S45, Analytic algebras and generalizations, preparation theorems, Commutative Algebra (math.AC), 01 natural sciences, Modifications, resolution of singularities (complex-analytic aspects), [MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Mathematics - Algebraic Geometry, Polynomials and rational functions of one complex variable, FOS: Mathematics, rank of an analytic map, Complex Variables (math.CV), 0101 mathematics, local analytic geometry, Algebraic Geometry (math.AG), Power series rings, Abhyankar-Jung's theorem, Completion of commutative rings, Mathematics - Complex Variables, Weierstrass preparation theorem, Valuations and their generalizations for commutative rings, Singularities in algebraic geometry, Mathematics - Commutative Algebra, formal power series, Nevanlinna theory, growth estimates, other inequalities of several complex variables, Valued fields, Formal neighborhoods in algebraic geometry

File Description: application/xml

Access URL: https://jep.centre-mersenne.org/item/10.5802/jep.173.pdf
http://arxiv.org/abs/2008.13130
https://arxiv-vanity.com/papers/2008.13130
https://jep.centre-mersenne.org/articles/10.5802/jep.173/
https://jep.centre-mersenne.org/item/10.5802/jep.173.pdf

Number of components of polynomial lemniscates: A problem of Erdös, Herzog, and Piranian: Number of components of polynomial lemniscates: a problem of Erdös, Herzog, and Piranian

Authors: Ghosh, Subhajit Ramachandran, Koushik

Source: Journal of Mathematical Analysis and Applications. 540:128571

Subject Terms: polynomials, Mathematics - Complex Variables, Mathematics - Classical Analysis and ODEs, Polynomials and rational functions of one complex variable, Capacity and harmonic measure in the complex plane, zeros, Potentials and capacities on other spaces, logarithmic capacity, 30, 31

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.13673

Generalizations of certain well known inequalities for polynomials: Generalization of certain well known inequalities for polynomials

Authors: V.K. Jain

Source: Publications de l'Institut Mathematique. 107:117-123

Subject Terms: Polynomials and rational functions of one complex variable, Inequalities in the complex plane, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://www.doiserbia.nb.rs/img/doi/0350-1302/2020/0350-13022021117J.pdf
https://zbmath.org/1045451
http://www.doiserbia.nb.rs/ft.aspx?id=0350-13022021117J
http://www.doiserbia.nb.rs/Article.aspx?id=0350-13022021117J

Inradius of random lemniscates

Authors: Manjunath Krishnapur Erik Lundberg Koushik Ramachandran

Source: Journal of Approximation Theory. 299:106018

Subject Terms: Mathematics - Complex Variables, concentration inequality, Probability (math.PR), Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, lemniscate, inradius, complex polynomial, 01 natural sciences, Bernstein inequality, Polynomials and rational functions of one complex variable, FOS: Mathematics, random polynomial, Random fields, 0101 mathematics, Complex Variables (math.CV), Mathematics, Mathematics - Probability, 30C10, 60G60, 31A15

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Access URL: http://arxiv.org/abs/2301.13424
https://zbmath.org/7818441
https://doi.org/10.1016/j.jat.2024.106018

Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions

Authors: Ajayi Adepoju, Jerome Mogbademu, Adesanmi Alao

Source: Proyecciones (Antofagasta, On line); Vol. 39 No. 3 (2020); 651-662 ; Proyecciones. Revista de Matemática; Vol. 39 Núm. 3 (2020); 651-662 ; 0717-6279 ; 10.22199/issn.0717-6279-2020-03

Subject Terms: Basic set, Faber polynomials, Faber regions, Faber curves, Composite set, Cannon set, Cannon function, Cannon sum, Constituent set, Effectiveness, 30A10, Inequalities in the complex plane, 30C10, Polynomials and rational functions of one complex variable, 30C20, Conformal mappings of special domains, 30D10, Representations of entire functions of one complex variable by series and integrals, 32A05, Power series, series of functions of several complex variables

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Relation: https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3599/3419; https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3599

Availability: https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3599
https://doi.org/10.22199/issn.0717-6279-2020-03-0040

Inverse Polynomial Images are Always Sets of Minimal Logarithmic Capacity: Inverse polynomial images are always sets of minimal logarithmic capacity

Authors: Klaus Schiefermayr

Source: Computational Methods and Function Theory. 16:375-386

Subject Terms: inverse polynomial image, Polynomials and rational functions of one complex variable, symmetry property, Capacity and harmonic measure in the complex plane, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, minimal logarithmic capacity, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6627827
https://doi.org/10.1007/s40315-015-0143-x
https://link.springer.com/article/10.1007/s40315-015-0143-x/fulltext.html
https://link.springer.com/content/pdf/10.1007%2Fs40315-015-0143-x.pdf
https://link.springer.com/article/10.1007/s40315-015-0143-x

The Pólya–Chebotarev problem and inverse polynomial images: The Pólya-Chebotarev problem and inverse polynomial images

Authors: Klaus Schiefermayr

Source: Acta Mathematica Hungarica. 142:80-94

Subject Terms: analytic Jordan arc, inverse polynomial image, Mathematics - Complex Variables, Polynomials and rational functions of one complex variable, the Green's function, FOS: Mathematics, Pólya-Chebotarev problem, Complex Variables (math.CV), 0101 mathematics, 16. Peace & justice, Padé approximation, logarithmic capacity, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/pdf/1306.6170
http://arxiv.org/abs/1306.6170
https://zbmath.org/6270607
https://doi.org/10.1007/s10474-013-0353-5
https://link.springer.com/article/10.1007/s10474-013-0353-5
https://rd.springer.com/article/10.1007/s10474-013-0353-5

Asymptotic expansions for polynomials orthogonal with respect to a complex non-constant weight function

Authors: R. Khabibullin A. Aptekarev

Source: Transactions of the Moscow Mathematical Society. 68:1-37

Subject Terms: Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Polynomials and rational functions of one complex variable, 0103 physical sciences, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/mosc/2007-68-00/S0077-1554-07-00167-7/S0077-1554-07-00167-7.pdf
https://zbmath.org/5354190
https://doi.org/10.1090/s0077-1554-07-00167-7
https://www.ams.org/mosc/2007-68-00/S0077-1554-07-00167-7/S0077-1554-07-00167-7.pdf
https://www.ams.org/journals/mosc/2007-68-00/S0077-1554-07-00167-7/home.html

On a conjecture of S.P. Robinson

Authors: Ruscheweyh, S Salinas, L

Source: Conicyt_qa
ANID
instacron:ANID
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Artículos CONICYT
CONICYT Chile
instacron:CONICYT
Articulos_ANID
Agencia Nacional de Investigación y Desarrollo

Subject Terms: Convex univalent, Applied Mathematics, Subordination, subordination, convex univalent, Cesàro means, 01 natural sciences, Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), prestarlike, Extremal problems for conformal and quasiconformal mappings, other methods, Polynomials and rational functions of one complex variable, Cesáro means, Prestarlike, 0101 mathematics, de la Vallée Poussin means, Analysis

File Description: application/xml

Access URL: https://zbmath.org/2235555
https://doi.org/10.1016/j.jmaa.2005.03.104
http://repositorio.conicyt.cl/handle/10533/176440
https://ui.adsabs.harvard.edu/abs/2005JMAA..312..548R/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0022247X05003100#!
https://core.ac.uk/display/82118957
https://www.sciencedirect.com/science/article/pii/S0022247X05003100
https://repositorio-qa.anid.cl/handle/10533/176440
http://hdl.handle.net/10533/176440
https://hdl.handle.net/10533/176440

On Littlewood's Constants: On Littlewood's constants

Authors: Beliaev, D. Smirnov, S.

Source: Bulletin of the London Mathematical Society, Vol. 37, No 05 (2005) pp. 719-726

Subject Terms: packing spectrum, polynomial, Capacity and harmonic measure in the complex plane, General theory of univalent and multivalent functions of one complex variable, harmonic measure, univalent function, 01 natural sciences, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Green function, Polynomials and rational functions of one complex variable, universal spectrum, ddc:510, 0101 mathematics

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/2242677
https://doi.org/10.1112/s0024609305004522
https://academic.oup.com/blms/article/37/5/719/344783
https://www.cambridge.org/core/journals/bulletin-of-the-london-mathematical-society/article/abs/on-littlewoods-constants/2C6451DF85EFDBF49A353526FE52A73D
https://unige.ch/~smirnov/papers/littlewood-j.pdf
http://www.diva-portal.org/smash/record.jsf?pid=diva2:435066
https://archive-ouverte.unige.ch/unige:12213
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024609305004522
https://ora.ox.ac.uk/objects/uuid:2d0d9555-4578-45ce-b62a-1cd0c1ff66fc
https://doi.org/10.1112/s0024609305004522
https://archive-ouverte.unige.ch/unige:12213
http://doc.rero.ch/record/300117/files/37-5-719.pdf

On polynomials orthogonal to all powers of a given polynomial on a segment

Authors: Fedor Pakovich

Source: Bulletin des Sciences Mathématiques. 129:749-774

Subject Terms: Moments, Algebraic functions, Mathematics(all), Cauchy type integrals, Mathematics - Complex Variables, Cauchy-type intergrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Polynomials, 01 natural sciences, polynomial moment problem, Galois groups, orthogonality, Mathematics - Classical Analysis and ODEs, Polynomials and rational functions of one complex variable, algebraic functions, Center problem, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Cacti, Orthogonality, Complex Variables (math.CV), 0101 mathematics, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane

File Description: application/xml

Access URL: http://arxiv.org/abs/math/0408019
https://zbmath.org/2244532
https://doi.org/10.1016/j.bulsci.2005.06.001
https://core.ac.uk/display/45696211
https://www.sciencedirect.com/science/article/pii/S000744970500059X
https://www.math.bgu.ac.il/~pakovich/Publications/bullfin.pdf
https://www.sciencedirect.com/science/article/abs/pii/S000744970500059X
http://www.math.bgu.ac.il/~pakovich/Publications/bullfin.pdf
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3124371

Conformal Mappings and Inequalities for Algebraic Polynomials. II: Conformal mappings and inequalities for algebraic polynomials

Authors: Vladimir Nikolaevich Dubinin

Source: Journal of Mathematical Sciences. 129:3823-3834

Subject Terms: univalent functions, Polynomials and rational functions of one complex variable, inequalities for polynomials, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1821769
https://link.springer.com/article/10.1007%2Fs10958-005-0318-5
https://link.springer.com/content/pdf/10.1007/s10958-005-0318-5.pdf