Geodesic
Coordinate description of analytic relations
Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 197-210

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
DOI : 10.21136/MB.2006.134091
Classification : 20L05, 34A30, 34C20, 34K05, 39B22, 39B72
Keywords: canonical form; Brandt groupoid; Ehresmann groupoid; transformation; differential equation; Abel functional equation; functional differential equation 
Neuman, František. Coordinate description of analytic relations. Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 197-210. doi: 10.21136/MB.2006.134091
@article{10_21136_MB_2006_134091,
     author = {Neuman, Franti\v{s}ek},
     title = {Coordinate description of analytic relations},
     journal = {Mathematica Bohemica},
     pages = {197--210},
     year = {2006},
     volume = {131},
     number = {2},
     doi = {10.21136/MB.2006.134091},
     mrnumber = {2242845},
     zbl = {1116.34006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134091/}
}
TY  - JOUR
AU  - Neuman, František
TI  - Coordinate description of analytic relations
JO  - Mathematica Bohemica
PY  - 2006
SP  - 197
EP  - 210
VL  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134091/
DO  - 10.21136/MB.2006.134091
LA  - en
ID  - 10_21136_MB_2006_134091
ER  - 
%0 Journal Article
%A Neuman, František
%T Coordinate description of analytic relations
%J Mathematica Bohemica
%D 2006
%P 197-210
%V 131
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.134091/
%R 10.21136/MB.2006.134091
%G en
%F 10_21136_MB_2006_134091

[1] E. Barvínek: O rozložení nulových bodů řešení lineární diferenciální rovnice $y^{\prime \prime }=Q(t)y$ a jejich derivací. Acta F. R. N. Univ. Comenian 5 (1961), 465–474.

[2] O. Borůvka: Linear Differential Transformations of the Second Order. The English Univ. Press, London, 1971. | MR

[3] B. Choczewski: On differentiable solutions of a functional equation. Ann. Polon. Math. 13 (1963), 133–138. | DOI | MR

[4] A. R. Forsyth: Invariants, covariants and quotient-derivatives associated with linear differential equations. Philos. Trans. Roy. Soc. London Ser. A 179 (1899), 377–489.

[5] M. Hasse, L. Michler: Theorie der Kategorien. VEB, Berlin, 1966. | MR

[6] M. Kuczma: Functional Equations in a Single Variable. PWN, 1968. | MR | Zbl

[7] M. Kuczma, B. Choczewski, R. Ger: Iterative Functional Equations. Cambridge Univ. Press, Cambridge, 1989. | MR

[8] E. E. Kummer: De generali quadam aequatione differentiali tertii ordinis (Progr. Evang. Königl. Stadtgymnasium Liegnitz 1834). J. Reine Angew. Math. (reprinted) 100 (1887), 1–10.

[9] E. Laguerre: Sur les équations differérentielles linéaires du troisième ordre. C. R. Acad. Sci. Paris 88 (1879), 116–118.

[10] F. Neuman: Geometrical approach to linear differential equations of the $n$-th order. Rend. Mat. 5 (1972), 579–602. | MR | Zbl

[11] F. Neuman: Simultaneous solutions of a system of Abel equations and differential equations with several deviations. Czechoslovak Math. J. 32 (1982), 488–494. | MR | Zbl

[12] F. Neuman: Criterion of global equivalence of linear differential equations. Proc. Roy. Soc. Edinburgh 97 A (1984), 217–221. | MR | Zbl

[13] F. Neuman: On Halphen and Laguerre-Forsyth canonical forms for linear differential equations. Archivum Math. (Brno) 26 (1990), 147–154. | MR

[14] F. Neuman: Transformations and canonical forms of functional-differential equations. Proc. Roy. Soc. Edinburgh 115 A (1990), 349–357. | MR

[15] F. Neuman: On a canonical parametrization of continuous functions. Opuscula Mathematica (Kraków) 6 (1990), 185–191. | MR | Zbl

[16] F. Neuman: Global Properties of Linear Ordinary Differential Equations. Mathematics and Its Applications (East European Series) 52, Kluwer Acad. Publ., Dordrecht, 1991. | MR | Zbl

[17] F. Neuman: On equivalence of linear functional-differential equations. Results in Mathematics 26 (1994), 354–359. | DOI | MR | Zbl

[18] F. Neuman: Algebraic aspects of transformations with an application to differential equations. Nonlinear Anal. 40 (2000), 505–511. | DOI | MR | Zbl

[19] F. Neuman: A general construction of linear differential equations with solutions of prescribed properties. Applied Math. Letters 17 (2004), 71–76. | DOI | MR | Zbl

[20] F. Neuman: Smooth and discrete systems—algebraic, analytic, and geometrical representations. Adv. Difference Equ. 2 (2004), 111–120. | MR | Zbl

[21] F. Neuman: Constructing and solving equations—inverse operations. Aequationes Math. 70 (2005), 77–87. | DOI | MR | Zbl

[22] E. J. Wilczynski: Projective Differential Geometry of Curves and Ruled Surfaces. Teubner, Leipzig, 1906.

Cité par Sources :