On spherical shells containing all the zeros of a quaternionic polynomial

Authors: Gradimir V. Milovanović, Abdullah Mir, Wasim Ahmad Thoker, Ashiq Hussain Bhat

Source: Analysis. 45:139-148

Subject Terms: Functions of hypercomplex variables and generalized variables, zeros, quaternionic polynomials

File Description: application/xml

Dirichlet Boundary Value Problems for Monogenic Functions of Prescribed Hölder Continuously Differentiable Data on Distinguishing Boundaries in Clifford Analysis: Dirichlet boundary value problems for monogenic functions of prescribed Hölder continuously differentiable data on distinguishing boundaries in Clifford analysis

Authors: Dao Viet Cuong, Wolfgang Tutschke, Le Hung Son

Source: Complex Analysis and Operator Theory. 19

Subject Terms: monogenic functions, Boundary value problems for linear first-order PDEs, Cauchy-Riemann system in higher dimensions, Functions of hypercomplex variables and generalized variables, boundary value problem, Boundary value and inverse problems for harmonic functions in higher dimensions, Clifford analysis

File Description: application/xml

Access URL: https://zbmath.org/8033586
https://doi.org/10.1007/s11785-025-01679-6

Bergman spaces and reproducing kernel for the biquaternionic Vekua equation

Authors: Víctor A. Vicente-Benítez

Source: Boletín de la Sociedad Matemática Mexicana. 31

Subject Terms: Bergman spaces and Fock spaces, Mathematics - Analysis of PDEs, Functions of hypercomplex variables and generalized variables, Bergman spaces, Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.), reproducing integral kernel, FOS: Mathematics, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), 30G20, 30G35, 30H20, 46E22, biquaternionic Vekua equation, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.07744
https://zbmath.org/8032028
https://doi.org/10.1007/s40590-025-00714-y

H-B Theorems of Cauchy Integral Operators in Clifford Analysis: H-B theorems of Cauchy integral operators in Clifford analysis

Authors: Yufeng Wang, Zhongxiang Zhang

Source: Advances in Applied Clifford Algebras. 35

Subject Terms: Functions of hypercomplex variables and generalized variables, Series solutions to PDEs, Cauchy integral operator, Clifford algebra, generalized Hölder norm, Harmonic, subharmonic, superharmonic functions in higher dimensions

File Description: application/xml

Spectral properties of the gradient operator with nonconstant coefficients

Authors: Colombo, F., Mantovani, F., Schlosser, P.

Source: Analysis and Mathematical Physics. 14

Subject Terms: Functional calculus for linear operators, Mathematics - Functional Analysis, Quaternionic operator theory, General theory of partial differential operators, Functions of hypercomplex variables and generalized variables, \(S\)-spectrum, boundary value problems, vector operators, FOS: Mathematics, Spectrum, resolvent, \(S\)-resolvent operator, Functional Analysis (math.FA)

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.17911

More About Bicomplex Möbius Transformations: Geometric, Algebraic and Analitical Aspects: More about bicomplex Möbius transformations: geometric, algebraic and analitical aspects

Authors: M. Elena Luna–Elizarrarás, Anatoly Golberg

Source: Advances in Applied Clifford Algebras. 34

Subject Terms: Functions of hypercomplex variables and generalized variables, Möbius transformation, bicomplex numbers

File Description: application/xml

Access URL: https://zbmath.org/7877967
https://doi.org/10.1007/s00006-024-01323-0

Discrete pseudo‐differential operators in hypercomplex analysis

Authors: Paula Cerejeiras, Uwe Kaehler, Simão Lucas

Source: Mathematical Methods in the Applied Sciences. 47:8025-8041

Subject Terms: functions of hypercomplex variables and generalized variables, discrete Dirac operators, discrete symbols, pseudodifferential operators, 0101 mathematics, 01 natural sciences

Access URL: http://hdl.handle.net/10773/43202

Quaternionic inner and outer functions

Authors: Alessandro Monguzzi, Giulia Sarfatti, Daniel Seco

Contributors: Ministerio de Economía y Competitividad (España)

Source: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)
e-Archivo: Repositorio Institucional de la Universidad Carlos III de Madrid
instname
Concrete Operators, Vol 6, Iss 1, Pp 44-57 (2019)

Subject Terms: Primary 30G35, Secondary 30H10, 30J05, functions of a quaternionic variable, inner and outer functions, primary 30g35, Matemáticas, Mathematics - Complex Variables, Secondary 30H10, 30J05, 02 engineering and technology, Functions of hypercomplex variables and generalized variables, Hardy spaces, Inner functions, outer functions, 01 natural sciences, QA1-939, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, secondary 30h10, 30j05, Complex Variables (math.CV), 0101 mathematics, Mathematics

File Description: application/pdf

Access URL: https://www.degruyter.com/downloadpdf/journals/conop/6/1/article-p44.pdf
http://arxiv.org/abs/1810.10070
https://hdl.handle.net/10016/32609
https://doaj.org/article/200136290f0f45b4bc5c3ef9c9b90d8d
https://boa.unimib.it/handle/10281/231558
https://flore.unifi.it/handle/2158/1153760

Errata to: The algebra of slice functions

Authors: Ghiloni, Riccardo, Perotti, Alessandro, Stoppato, Caterina

Source: Transactions of the American Mathematical Society.

Subject Terms: 30G35 Functions of hypercomplex variables and generalized variables, 17D05 Alternative rings, 32A30 Other generalizations of function theory of one complex variable, 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: https://hdl.handle.net/2158/1246758
https://doi.org/10.1090/tran/8574

Electrostatic Fields in Some Special Inhomogeneous Media and New Generalizations of the Cauchy–Riemann System: Electrostatic fields in some special inhomogeneous media and new generalizations of the Cauchy-Riemann system

Authors: Dmitry Bryukhov

Source: Advances in Applied Clifford Algebras. 31

Subject Terms: Euler-Poisson-Darboux equations, radially holomorphic potential, elliptic Euler-Poisson-Darboux equation in cylindrical coordinates, Maxwell equations, Functions of hypercomplex variables and generalized variables, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Composite media, random media in optics and electromagnetic theory, electric field gradient tensor, 0101 mathematics, harmonic meridional mappings of the second kind, Electro- and magnetostatics, \( \alpha \)-meridional, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7384727
https://doi.org/10.1007/s00006-021-01163-2
https://link.springer.com/article/10.1007/s00006-021-01163-2
https://link.springer.com/content/pdf/10.1007/s00006-021-01163-2.pdf

Three-dimensional Analogue of Kolosov–Muskhelishvili Formulae

Authors: Grigor’ev, Yuri^Aff5

Contributors: Bernstein, Swanhild, editor^Aff1, Kähler, Uwe, editor^Aff2, Sabadini, Irene, editor^Aff3, Sommen, Franciscus, editor^Aff4

Source: Modern Trends in Hypercomplex Analysis. :203-215

Uncertainty principle for measurable sets and signal recovery in quaternion domains

Authors: Yan Yang, Cuiming Zou, Kit Ian Kou

Source: Mathematical Methods in the Applied Sciences. 40:3892-3900

Subject Terms: FOS: Computer and information sciences, uncertainty principle, Functions of hypercomplex variables and generalized variables, Computer Science - Information Theory, Information Theory (cs.IT), quaternion Fourier transform, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology

File Description: application/xml

Access URL: http://arxiv.org/pdf/1608.05543
http://arxiv.org/abs/1608.05543
https://zbmath.org/6750454
https://doi.org/10.1002/mma.4271
https://www.arxiv.org/abs/1608.05543
https://arxiv.org/pdf/1608.05543.pdf
https://arxiv.org/abs/1608.05543
https://onlinelibrary.wiley.com/doi/full/10.1002/mma.4271
http://dblp.uni-trier.de/db/journals/corr/corr1608.html#KouYZ16
https://arxiv.org/pdf/1608.05543
http://ui.adsabs.harvard.edu/abs/2017MMAS...40.3892K/abstract
https://dblp.uni-trier.de/db/journals/corr/corr1608.html#KouYZ16

The algebra of slice functions

Authors: Ghiloni R., Perotti A., Stoppato C.

Source: Transactions of the American Mathematical Society. 369:4725-4762

Subject Terms: Primary 30G35, Secondary 17D05, 32A30, 30C15, Mathematics - Complex Variables, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, 30G35 Functions of hypercomplex variables and generalized variables, 17D05 Alternative rings, 32A30 Other generalizations of function theory of one complex variable, 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable, Complex Variables (math.CV), 0101 mathematics, 01 natural sciences, 6. Clean water

File Description: application/pdf

Access URL: http://arxiv.org/abs/1506.03749
https://ui.adsabs.harvard.edu/abs/2015arXiv150603749G/abstract
https://arxiv.org/abs/1506.03749
https://arxiv.org/pdf/1506.03749.pdf
https://flore.unifi.it/handle/2158/1038167
https://www.ams.org/journals/tran/2017-369-07/S0002-9947-2016-06816-6/

The Existence of Cauchy Kernels of Kravchenko-Generalized Dirac Operators: The existence of Cauchy kernels of Kravchenko-generalized Dirac operators

Authors: Doan Cong Dinh

Source: Advances in Applied Clifford Algebras. 31

Subject Terms: static Maxwell system, Functions of hypercomplex variables and generalized variables, generalized monogenic functions, generalized Cauchy kernel, 0103 physical sciences, 0101 mathematics, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7300839
https://doi.org/10.1007/s00006-020-01106-3
https://link.springer.com/article/10.1007/s00006-020-01106-3
https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=202102280912623426

Dirac Operators with Gradient Potentials and Related Monogenic Functions: Dirac operators with gradient potentials and related monogenic functions

Authors: Daowei Ma, Longfei Gu

Source: Complex Analysis and Operator Theory. 14

Subject Terms: Functions of hypercomplex variables and generalized variables, Dirac operators, 0101 mathematics, gradient potentials, 01 natural sciences, Clifford analysis

File Description: application/xml

Access URL: https://zbmath.org/7229688
https://doi.org/10.1007/s11785-020-01010-5
https://link.springer.com/article/10.1007/s11785-020-01010-5

Three-dimensional Quaternionic Analogue of the Kolosov–Muskhelishvili Formulae

Authors: Grigor’ev, Yuri^Aff5

Contributors: Bernstein, Swanhild, editor^Aff1, Kähler, Uwe, editor^Aff2, Sabadini, Irene, editor^Aff3, Sommen, Frank, editor^Aff4

Source: Hypercomplex Analysis: New Perspectives and Applications. :145-166

Tighter Uncertainty Principles Based on Quaternion Fourier Transform: Tighter uncertainty principles based on quaternion Fourier transform

Authors: Yan Yang, Pei Dang, Tao Qian

Source: Advances in Applied Clifford Algebras. 26:479-497

Subject Terms: Signal theory (characterization, reconstruction, filtering, etc.), Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Functions of hypercomplex variables and generalized variables, uncertainty principles, quaternion Fourier transform, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/6581630
https://doi.org/10.1007/s00006-015-0579-0
https://link.springer.com/content/pdf/10.1007%2Fs00006-015-0579-0.pdf
https://link.springer.com/article/10.1007/s00006-015-0579-0

On Bers Generating Functions for First Order Systems of Mathematical Physics: On Bers generating functions for first order systems of mathematical physics

Authors: P T Marco Ramirez, Vladislav V. Kravchenko

Source: Advances in Applied Clifford Algebras. 21:547-559

Subject Terms: pseudoanalytic function, Maxwell's system, FOS: Physical sciences, Mathematical Physics (math-ph), 30G20, 30G35, 35F05, 76M40, 78A25, 81Q05, 01 natural sciences, inhomogeneous medium, Maxwell equations, force-free field, Functions of hypercomplex variables and generalized variables, 0103 physical sciences, Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.), Dirac equation, 0101 mathematics, Mathematical Physics

File Description: application/xml

Access URL: http://arxiv.org/pdf/1001.0552
http://arxiv.org/abs/1001.0552
https://zbmath.org/5959933
https://doi.org/10.1007/s00006-010-0261-5
https://link.springer.com/content/pdf/10.1007%2Fs00006-010-0261-5.pdf
https://link.springer.com/article/10.1007%2Fs00006-010-0261-5

On the treatment of fluid problems by methods of Clifford analysis

Authors: Klaus Gürlebeck, Wolfgang Sprössig

Source: Notes on Numerical Fluid Mechanics (NNFM) ISBN: 9783322898401

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Functions of hypercomplex variables and generalized variables, Basic methods in fluid mechanics, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://econpapers.repec.org/RePEc:eee:matcom:v:44:y:1997:i:4:p:401-413
https://rd.springer.com/chapter/10.1007/978-3-322-89838-8_40
https://www.sciencedirect.com/science/article/pii/S0378475497000669
https://link.springer.com/chapter/10.1007%2F978-3-322-89838-8_40
https://ideas.repec.org/a/eee/matcom/v44y1997i4p401-413.html

Clifford algebra-valued orthogonal polynomials in Euclidean space

Authors: Franciscus Sommen, Fred Brackx, N. De Schepper

Source: Journal of Approximation Theory. 137:108-122

Subject Terms: weight functions, Mathematics(all), Numerical Analysis, Orthogonal polynomials, Functions of hypercomplex variables and generalized variables, Applied Mathematics, Special polynomials in general fields, 0101 mathematics, Approximation in the complex plane, orthogonal polynomials, 01 natural sciences, Clifford analysis, Analysis

File Description: application/xml

Access URL: https://zbmath.org/2235697
https://doi.org/10.1016/j.jat.2005.08.004
https://biblio.ugent.be/publication/343779
https://dialnet.unirioja.es/servlet/articulo?codigo=1338519
https://dblp.uni-trier.de/db/journals/jat/jat137.html#BrackxSS05
https://www.sciencedirect.com/science/article/abs/pii/S0021904505001449
https://core.ac.uk/display/82787298
https://www.sciencedirect.com/science/article/pii/S0021904505001449