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Boundedness of solutions for a class of impact oscillators with time-denpendent polynomial potentials
The Fueter primitive of biaxially monogenic functions
1. | Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano |
2. | Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133 Milano |
3. | Clifford Research Group, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Gent |
References:
[1] |
F. Brackx, R. Delanghe and F. Sommen, "Clifford Analysis,", Pitman Res. Notes in Math., (1982).
|
[2] |
F. Colombo, I. Sabadini and F. Sommen, The Fueter mapping theorem in integral form and the $\mathcalF$-functional calculus,, Math. Methods Appl. Sci., 33 (2010), 2050.
doi: 10.1002/mma.1315. |
[3] |
F. Colombo, I. Sabadini and F. Sommen, The inverse Fueter mapping theorem,, Commun. Pure Appl. Anal., 10 (2011), 1165.
doi: 10.3934/cpaa.2011.10.1165. |
[4] |
F. Colombo, I. Sabadini and F. Sommen, The inverse Fueter mapping theorem in integral form using spherical monogenics,, Israel J. Math., 194 (2013), 485.
doi: 10.1007/s11856-012-0090-4. |
[5] |
F. Colombo, I. Sabadini, F. Sommen and D. C. Struppa, "Analysis of Dirac Systems and Computational Algebra,", Progress in Mathematical Physics, (2004).
|
[6] |
F. Colombo, I. Sabadini and D. C. Struppa, "Noncommutative Functional Calculus. Theory and Applications of Slice Hyperholomorphic Functions,", Progress in Mathematics, (2011).
|
[7] |
A. K. Common and F. Sommen, Axial monogenic functions from holomorphic functions,, J. Math. Anal. Appl., 179 (1993), 610.
doi: 10.1006/jmaa.1993.1372. |
[8] |
R. Delanghe, F. Sommen and V. Souček, "Clifford Algebra and Spinor-valued Functions,", Mathematics and Its Applications 53, (1992).
|
[9] |
R. Fueter, Die Funktionentheorie der Differentialgleichungen $\Delta u = 0$ und $\Delta\Delta u = 0$ mit vier reellen Variablen,, Comm. Math. Helv., 7 (1934), 307.
|
[10] |
J. E. Gilbert and M. A. M. Murray, "Clifford Algebras and Dirac Operators in Harmonic Analysis,", Cambridge studies in advanced mathematics n. 26 (1991)., (1991).
|
[11] |
I. S. Gradshteyn and I. M. Ryzhik, "Table of Integrals, Series, and Products,", Academic Press LTD, (2000).
|
[12] |
K. Gürlebeck, K. Habetha and W. Sprößig, "Holomorphic Functions in the Plane and $n$-dimensional Space,", Birkh\, (2008).
|
[13] |
H. Hochstadt, "The functions of Mathematical Physics,", Pure Appl. Math., (1971).
|
[14] |
G. Jank and F. Sommen, Clifford analysis, biaxial symmetry and pseudoanalytic functions,, Compl. Var. Theory Appl., 13 (1990), 195.
|
[15] |
K. I. Kou, T. Qian and F. Sommen, Generalizations of Fueter's theorem,, Meth. Appl. Anal., 9 (2002), 273.
|
[16] |
D. Pena-Pena, "Cauchy-Kowalevski Extensions, Fueter's Theorems and Boundary Values of Special Systems in Clifford Analysis,", PhD Dissertation, (2008). Google Scholar |
[17] |
D. Pena-Pena, T. Qian and F. Sommen, An alternative proof of Fueter's theorem,, Complex Var. Elliptic Equ., 51 (2006), 913.
doi: 10.1080/17476930600667650. |
[18] |
T. Qian, Generalization of Fueter's result to $R^{n+1}$,, Rend. Mat. Acc. Lincei, 8 (1997), 111.
|
[19] |
T. Qian, Fourier analysis on a starlike Lipschitz aurfaces,, J. Funct. Anal., 183 (2001), 370.
doi: 10.1006/jfan.2001.3750. |
[20] |
T. Qian, Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space,, Math. Ann., 310 (1998), 601.
|
[21] |
T. Qian and F. Sommen, Deriving harmonic functions in higher dimensional spaces,, Zeit. Anal. Anwen., 2 (2003), 1.
|
[22] |
M. Sce, Osservazioni sulle serie di potenze nei moduli quadratici,, Atti Acc. Lincei Rend. Fisica, 23 (1957), 220.
|
[23] |
F. Sommen, On a generalization of Fueter's theorem,, Zeit. Anal. Anwen., 19 (2000), 899.
|
show all references
References:
[1] |
F. Brackx, R. Delanghe and F. Sommen, "Clifford Analysis,", Pitman Res. Notes in Math., (1982).
|
[2] |
F. Colombo, I. Sabadini and F. Sommen, The Fueter mapping theorem in integral form and the $\mathcalF$-functional calculus,, Math. Methods Appl. Sci., 33 (2010), 2050.
doi: 10.1002/mma.1315. |
[3] |
F. Colombo, I. Sabadini and F. Sommen, The inverse Fueter mapping theorem,, Commun. Pure Appl. Anal., 10 (2011), 1165.
doi: 10.3934/cpaa.2011.10.1165. |
[4] |
F. Colombo, I. Sabadini and F. Sommen, The inverse Fueter mapping theorem in integral form using spherical monogenics,, Israel J. Math., 194 (2013), 485.
doi: 10.1007/s11856-012-0090-4. |
[5] |
F. Colombo, I. Sabadini, F. Sommen and D. C. Struppa, "Analysis of Dirac Systems and Computational Algebra,", Progress in Mathematical Physics, (2004).
|
[6] |
F. Colombo, I. Sabadini and D. C. Struppa, "Noncommutative Functional Calculus. Theory and Applications of Slice Hyperholomorphic Functions,", Progress in Mathematics, (2011).
|
[7] |
A. K. Common and F. Sommen, Axial monogenic functions from holomorphic functions,, J. Math. Anal. Appl., 179 (1993), 610.
doi: 10.1006/jmaa.1993.1372. |
[8] |
R. Delanghe, F. Sommen and V. Souček, "Clifford Algebra and Spinor-valued Functions,", Mathematics and Its Applications 53, (1992).
|
[9] |
R. Fueter, Die Funktionentheorie der Differentialgleichungen $\Delta u = 0$ und $\Delta\Delta u = 0$ mit vier reellen Variablen,, Comm. Math. Helv., 7 (1934), 307.
|
[10] |
J. E. Gilbert and M. A. M. Murray, "Clifford Algebras and Dirac Operators in Harmonic Analysis,", Cambridge studies in advanced mathematics n. 26 (1991)., (1991).
|
[11] |
I. S. Gradshteyn and I. M. Ryzhik, "Table of Integrals, Series, and Products,", Academic Press LTD, (2000).
|
[12] |
K. Gürlebeck, K. Habetha and W. Sprößig, "Holomorphic Functions in the Plane and $n$-dimensional Space,", Birkh\, (2008).
|
[13] |
H. Hochstadt, "The functions of Mathematical Physics,", Pure Appl. Math., (1971).
|
[14] |
G. Jank and F. Sommen, Clifford analysis, biaxial symmetry and pseudoanalytic functions,, Compl. Var. Theory Appl., 13 (1990), 195.
|
[15] |
K. I. Kou, T. Qian and F. Sommen, Generalizations of Fueter's theorem,, Meth. Appl. Anal., 9 (2002), 273.
|
[16] |
D. Pena-Pena, "Cauchy-Kowalevski Extensions, Fueter's Theorems and Boundary Values of Special Systems in Clifford Analysis,", PhD Dissertation, (2008). Google Scholar |
[17] |
D. Pena-Pena, T. Qian and F. Sommen, An alternative proof of Fueter's theorem,, Complex Var. Elliptic Equ., 51 (2006), 913.
doi: 10.1080/17476930600667650. |
[18] |
T. Qian, Generalization of Fueter's result to $R^{n+1}$,, Rend. Mat. Acc. Lincei, 8 (1997), 111.
|
[19] |
T. Qian, Fourier analysis on a starlike Lipschitz aurfaces,, J. Funct. Anal., 183 (2001), 370.
doi: 10.1006/jfan.2001.3750. |
[20] |
T. Qian, Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space,, Math. Ann., 310 (1998), 601.
|
[21] |
T. Qian and F. Sommen, Deriving harmonic functions in higher dimensional spaces,, Zeit. Anal. Anwen., 2 (2003), 1.
|
[22] |
M. Sce, Osservazioni sulle serie di potenze nei moduli quadratici,, Atti Acc. Lincei Rend. Fisica, 23 (1957), 220.
|
[23] |
F. Sommen, On a generalization of Fueter's theorem,, Zeit. Anal. Anwen., 19 (2000), 899.
|
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