Rate of rational approximation and asymptotic monogeneity of functions at points of the finite porosity of a compact set

Authors: D. Ya. Danchenko

Source: Journal of Mathematical Sciences. 126:1580-1585

Subject Terms: Approximation by rational functions, Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), asymptotic derivative, Monogenic and polygenic functions of one complex variable, porosity, porosity measure, monogenic function, 0101 mathematics, Approximation in the complex plane, rational approximation, finite-porosity condition, 01 natural sciences, asymptotically monogenic function

File Description: application/xml

Access URL: https://zbmath.org/2193560
https://doi.org/10.1007/s10958-005-0046-x
https://rd.springer.com/article/10.1007/s10958-005-0046-x
https://link.springer.com/article/10.1007/s10958-005-0046-x

Solution of the Truncated Parabolic Moment Problem: Solution of the truncated parabolic moment problem

Authors: Raúl E. Curto, Lawrence A. Fialkow

Source: Integral Equations and Operator Theory. 50:169-196

Subject Terms: Trigonometric moment problems in one variable harmonic analysis, 47A57, 44A60, 42A70, 30A05, 01 natural sciences, parabolic moment problem, moment matrix extension, Functional Analysis (math.FA), Mathematics - Functional Analysis, Monogenic and polygenic functions of one complex variable, Moment problems, FOS: Mathematics, Hermitian, skew-Hermitian, and related matrices, Dilations, extensions, compressions of linear operators, flat extensions of positive matrices, 0101 mathematics, Linear operator methods in interpolation, moment and extension problems

File Description: application/xml

Access URL: http://www.cs.newpaltz.edu/~fialkowl/files/parabola.pdf
http://arxiv.org/pdf/math/0507069
http://arxiv.org/abs/math/0507069
https://zbmath.org/2138208
https://doi.org/10.1007/s00020-003-1275-3
http://www.math.uiowa.edu/~rcurto/tcmp9.pdf
https://link.springer.com/article/10.1007%2Fs00020-004-1340-6
http://www.cs.newpaltz.edu/~fialkowl/files/parabola.pdf
http://homepage.math.uiowa.edu/~rcurto/tcmp9.pdf
https://link.springer.com/content/pdf/10.1007/s00020-003-1275-3.pdf
https://www.math.uiowa.edu/~rcurto/tcmp9.pdf

A Generalization of Men'shov's Theorem on Functions Satisfying Condition K″: A generalization of Men'shov's theorem on functions satisfying the condition \(K''\).

Authors: D. S. Telyakovskii

Source: Mathematical Notes. 76:534-545

Subject Terms: Monogenic and polygenic functions of one complex variable, holomorphic functions, dilation, mapping, 0101 mathematics, 01 natural sciences, Analytic continuation of functions of one complex variable, triple of pairwise non-colinear rays

File Description: application/xml

Access URL: https://zbmath.org/2177664
https://doi.org/10.1023/b:matn.0000043483.90707.4d
https://link.springer.com/content/pdf/10.1023/B:MATN.0000043483.90707.4d.pdf
https://link.springer.com/article/10.1023/B:MATN.0000043483.90707.4d

On Quaternionic Analysis and its Modifications: On quaternionic analysis and its modifications

Authors: Peter Zeilinger, Heinz Leutwiler

Source: Computational Methods and Function Theory. 4:159-182

Subject Terms: quaternions, Monogenic and polygenic functions of one complex variable, Functions of hypercomplex variables and generalized variables, Dirac operator, 0103 physical sciences, generalized function theory, 0101 mathematics, 01 natural sciences, Conformal metrics (hyperbolic, Poincaré, distance functions), hyperbolic metric

File Description: application/xml

Access URL: https://zbmath.org/2104122
https://doi.org/10.1007/bf03321063
https://link.springer.com/article/10.1007/BF03321063
https://link.springer.com/content/pdf/10.1007/BF03321063.pdf

An operator corona theorem

Authors: Sergei Treil

Source: Indiana University Mathematics Journal. 53:1765-1784

Subject Terms: Monogenic and polygenic functions of one complex variable, Corona theorem, Toeplitz operators, Hankel operators, Wiener-Hopf operators, 0101 mathematics, 01 natural sciences, \(H^p\)-classes

File Description: application/xml

Access URL: https://zbmath.org/2211026
https://doi.org/10.1512/iumj.2004.53.2640
http://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=2640&year=2004&volume=53
https://core.ac.uk/display/100716246
https://www.math.brown.edu/~treil/papers/OperCorona/oper.pdf

On One Criterion for the Holomorphy of an Arbitrary Mapping of a Plane Domain into a Plane: On one criterion for the holomorphy of an arbitrary mapping of a plane domain into a plane

Authors: M. T. Brodovic

Source: Ukrainian Mathematical Journal. 55:1395-1409

Subject Terms: Monogenic and polygenic functions of one complex variable, 0102 computer and information sciences, mapping, 0101 mathematics, 01 natural sciences, criterion of holomorphy

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/B%3AUKMA.0000018003.78182.b5

Hyperholomorphic Functions: Hyperholomorphic functions

Authors: Eriksson-Bique, Sirkka-Liisa, Leutwiler, Heinz

Source: Computational Methods and Function Theory. 1:179-192

Subject Terms: quaternions, Monogenic and polygenic functions of one complex variable, Functions of hypercomplex variables and generalized variables, hyperbolic metrics, hyperholomorphic functions, 0103 physical sciences, generalized function theory, 0101 mathematics, 01 natural sciences, Conformal metrics (hyperbolic, Poincaré, distance functions)

File Description: application/xml

On Integral Representations of an Axisymmetric Potential and the Stokes Flow Function in Domains of the Meridian Plane. II: On integral representations of an axisymmetric potential and the Stokes flow function in domains of the meridian plane. I

Authors: S. A. Plaksa

Source: Ukrainian Mathematical Journal. 53:938-950

Subject Terms: Monogenic and polygenic functions of one complex variable, axisymmetric potential, integral representations, axially symmetric potential, Integral representations, integral operators, integral equations methods in two dimensions, Free-surface potential flows for incompressible inviscid fluids, Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions, Stokes flow, 0101 mathematics, integral representation, 01 natural sciences, Stokes and related (Oseen, etc.) flows, Jordan boundary

File Description: application/xml

Access URL: https://zbmath.org/1646183
https://doi.org/10.1023/a:1012578200291
https://link.springer.com/content/pdf/10.1023/A:1013351918523.pdf
https://link.springer.com/article/10.1023/A%3A1013351918523
https://link.springer.com/content/pdf/10.1023/A:1012578200291.pdf

on integral representations of an axisymmetric potential and the stokes flow function in domains of the meridian plane ii: On integral representations of an axisymmetric potential and the Stokes flow function in domains of the meridian plane. I

Authors: S. A. Plaksa

Source: Ukrainian Mathematical Journal. 53(5):726-743

Subject Terms: Monogenic and polygenic functions of one complex variable, axisymmetric potential, integral representations, axially symmetric potential, Integral representations, integral operators, integral equations methods in two dimensions, Free-surface potential flows for incompressible inviscid fluids, Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions, Stokes flow, integral representation, Stokes and related (Oseen, etc.) flows, Jordan boundary

File Description: application/xml

Access URL: https://zbmath.org/1646183
https://doi.org/10.1023/a:1012578200291
https://link.springer.com/content/pdf/10.1023/A:1013351918523.pdf
https://link.springer.com/article/10.1023/A%3A1013351918523
https://link.springer.com/content/pdf/10.1023/A:1012578200291.pdf

A New Morera-Type Theorem on a Unit Disk: A new Morera-type theorem on the unit disk

Authors: V. E. Silenko

Source: Ukrainian Mathematical Journal. 53:317-322

Subject Terms: Monogenic and polygenic functions of one complex variable, Iwasawa decomposition, 0101 mathematics, Morera theorem, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1668433
https://doi.org/10.1023/a:1010485508280
https://link.springer.com/content/pdf/10.1023/A:1010485508280.pdf
https://link.springer.com/article/10.1023/A:1010485508280

a new morera type theorem on a unit disk: A new Morera-type theorem on the unit disk

Authors: V. E. Silenko

Source: Ukrainian Mathematical Journal. 53(2):317-322

Subject Terms: Monogenic and polygenic functions of one complex variable, Iwasawa decomposition, Morera theorem

File Description: application/xml

Access URL: https://zbmath.org/1668433
https://doi.org/10.1023/a:1010485508280
https://link.springer.com/content/pdf/10.1023/A:1010485508280.pdf
https://link.springer.com/article/10.1023/A:1010485508280

On directional monogeneity sets

Authors: Diab, F.M.

Source: Ukrainian Mathematical Journal. 49:569-575

Subject Terms: Monogenic and polygenic functions of one complex variable, complex \(z\)-plane, topological space, set of first category, directional monogeneity set, 0101 mathematics, ????????????, 01 natural sciences, Baire property

File Description: application/xml

Access URL: http://dspace.nbuv.gov.ua/xmlui/bitstream/123456789/156916/1/45-Diab.pdf
https://link.springer.com/article/10.1007/BF02487319
https://link.springer.com/content/pdf/10.1007/BF02487319.pdf
http://dspace.nbuv.gov.ua/handle/123456789/156916

A weakened asymptotic monogeny condition

Authors: D. S. Telyakovskii

Source: Mathematical Notes. 60:681-687

Subject Terms: monogenic functions, Monogenic and polygenic functions of one complex variable, 0103 physical sciences, Menshov's theorem, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF02305161

An extremum problem related to Morera's theorem: An extremum Problem related to Morera's theorem

Authors: V. V. Volchkov

Source: Mathematical Notes. 60:606-610

Subject Terms: Monogenic and polygenic functions of one complex variable, description of holomorphic functions, Morera's theorem, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF02305151

Potential fields with axial symmetry and algebras of monogenic functions of vector variables. III: Potential fields with axial symmetry and algebras of monogenic functions of vector variable. III

Authors: S. A. Plaksa, I. P. Mel’nichenko

Source: Ukrainian Mathematical Journal. 49:253-268

Subject Terms: integral Cauchy formulas, analogy of symmetry principle, Monogenic and polygenic functions of one complex variable, criterion of monogeneity of function, 4. Education, monogenic function, 0101 mathematics, Runge approximation theorems, uniqueness theorems, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1395429
https://doi.org/10.1007/bf02529493
https://link.springer.com/article/10.1007%2FBF02529493

Extension of the Unit Disk Gyrogroup into the Unit Ball of Any Real Inner Product Space: Extension of the unit disk gyrogroup into the unit ball of any real inner product space

Authors: Abraham A. Ungar

Source: Journal of Mathematical Analysis and Applications. 202:1040-1057

Subject Terms: Special relativity, Loops, quasigroups, Extensions, wreath products, and other compositions of groups, Bruck loops, Applied Mathematics, real inner product spaces, 01 natural sciences, generalized Poincaré metric, Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.), open balls, Monogenic and polygenic functions of one complex variable, \(k\)-loops, hyperbolic spaces, gyrogroups, Möbius transformations, Structure and representation of the Lorentz group, motion groups, 0101 mathematics, Analysis

File Description: application/xml

Access URL: https://core.ac.uk/display/82792035
https://www.sciencedirect.com/science/article/pii/S0022247X96903595

Bi-axial Gegenbauer Functions of the Second Kind: Bi-axial Gegenbauer functions of the second kind

Authors: Alan K. Common

Source: Journal of Mathematical Analysis and Applications. 190:725-737

Subject Terms: Monogenic and polygenic functions of one complex variable, Applied Mathematics, bi-axial monogenic functions, bi-axial Gegenbauer polynomials, Analysis

File Description: application/xml

Access URL: https://zbmath.org/762185
https://doi.org/10.1006/jmaa.1995.1106
https://kar.kent.ac.uk/19766/
https://www.sciencedirect.com/science/article/pii/S0022247X85711067
https://core.ac.uk/display/82829603

Special Bi-Axial Monogenic Functions: Special bi-axial monogenic functions

Authors: Ak Common, Franciscus Sommen

Source: Journal of Mathematical Analysis and Applications. 185:189-206

Subject Terms: Monogenic and polygenic functions of one complex variable, Applied Mathematics, bi-axial functions, monogenic function, 0101 mathematics, 01 natural sciences, Analysis

File Description: application/xml

Access URL: https://zbmath.org/737220
https://doi.org/10.1006/jmaa.1994.1241
https://www.sciencedirect.com/science/article/pii/S0022247X84712418
https://core.ac.uk/display/55786862
https://biblio.ugent.be/publication/198650
https://kar.kent.ac.uk/20465/

The holomorphic automorphism group of the complex disk

Authors: Ungar, Abraham A.

Source: Aequationes Mathematicae. 47:240-254

Subject Terms: Special relativity, Extensions, wreath products, and other compositions of groups, Loops, quasigroups, gyrosemidirect product, holomorphic permutation, rotation, 01 natural sciences, Article, gyration, 510.mathematics, Monogenic and polygenic functions of one complex variable, Structure and representation of the Lorentz group, 0103 physical sciences, Spaces of bounded analytic functions of one complex variable, 0101 mathematics, gyrogroup, Algebras of holomorphic functions of several complex variables

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://eudml.org/doc/137584
https://link.springer.com/article/10.1007/BF01832962

New differentiability criteria for complex-valued functions

Authors: É. O. Alikulov

Source: Ukrainian Mathematical Journal. 46:343-351

Subject Terms: Monogenic and polygenic functions of one complex variable, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/830569
https://doi.org/10.1007/bf01060404
https://link.springer.com/article/10.1007/BF01060404