
-
Previous Article
On optimal autocorrelation inequalities on the real line
- CPAA Home
- This Issue
-
Next Article
Analytical and numerical monotonicity results for discrete fractional sequential differences with negative lower bound
Isomorphism between one-dimensional and multidimensional finite difference operators
Jacobs University, Campus Ring 1, 28759 Bremen, Germany, Saint-Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia |
Finite difference operators are widely used for the approximation of continuous ones. It is well known that the analysis of continuous differential operators may strongly depend on their dimensions. We will show that the finite difference operators generate the same algebra, regardless of their dimension.
References:
[1] |
V. V. Bavula,
The algebra of integro-differential operators on an affine line and its modules, J. Pure Appl. Algebra, 217 (2013), 495-529.
doi: 10.1016/j.jpaa.2012.06.024. |
[2] |
K. Davidson, C*-Algebras by Example, American Mathematical Society and Fields Institute, 1997.
doi: 10.1090/fim/006. |
[3] |
L. C. Evans, Partial Differential Equations, 2$^nd$ edition, American Mathematical Society, Providence, Rhode Island, 2010. Google Scholar |
[4] |
J. G. Glimm,
On a certain class of operator algebras, Trans. Am. Math. Soc., 95 (1960), 318-340.
doi: 10.2307/1993294. |
[5] |
L. Guo and W. Keigher,
On differential Rota-Baxter algebras, J. Pure Appl. Algebra, 212 (2008), 522-540.
doi: 10.1016/j.jpaa.2007.06.008. |
[6] |
L. Guo, G. Regensburger and M. Rosenkranz,
On integro-differential algebras, J. Pure Appl. Algebra, 218 (2014), 456-473.
doi: 10.1016/j.jpaa.2013.06.015. |
[7] |
R. Hoegh-Krohn and T. Skjelbred,
Classification of C*-algebras admitting ergodic actions of the two-dimensional torus, J. Reine Angew. Math., 328 (1981), 1-8.
doi: 10.1515/crll.1981.328.1. |
[8] |
M. Rordam, F. Larsen and N. J. Laustsen, An Introduction to K-Theory for C*-Algebras, Cambridge University Press, 2000.
![]() |
[9] |
M. Rosenkranz,
A new symbolic method for solving linear two-point boundary value problems on the level of operators, J. Symb. Comput, 39 (2005), 171-199.
doi: 10.1016/j.jsc.2004.09.004. |
[10] |
M. Tenenbaum and H. Pollard, Ordinary Differential Equations, Dover Publications Inc., 2012. Google Scholar |
[11] |
H. S. Yin,
A simple proof of the classification of rational rotation C*-algebras, P. Am. Math. Soc., 98 (1986), 469-470.
doi: 10.2307/2046204. |
show all references
References:
[1] |
V. V. Bavula,
The algebra of integro-differential operators on an affine line and its modules, J. Pure Appl. Algebra, 217 (2013), 495-529.
doi: 10.1016/j.jpaa.2012.06.024. |
[2] |
K. Davidson, C*-Algebras by Example, American Mathematical Society and Fields Institute, 1997.
doi: 10.1090/fim/006. |
[3] |
L. C. Evans, Partial Differential Equations, 2$^nd$ edition, American Mathematical Society, Providence, Rhode Island, 2010. Google Scholar |
[4] |
J. G. Glimm,
On a certain class of operator algebras, Trans. Am. Math. Soc., 95 (1960), 318-340.
doi: 10.2307/1993294. |
[5] |
L. Guo and W. Keigher,
On differential Rota-Baxter algebras, J. Pure Appl. Algebra, 212 (2008), 522-540.
doi: 10.1016/j.jpaa.2007.06.008. |
[6] |
L. Guo, G. Regensburger and M. Rosenkranz,
On integro-differential algebras, J. Pure Appl. Algebra, 218 (2014), 456-473.
doi: 10.1016/j.jpaa.2013.06.015. |
[7] |
R. Hoegh-Krohn and T. Skjelbred,
Classification of C*-algebras admitting ergodic actions of the two-dimensional torus, J. Reine Angew. Math., 328 (1981), 1-8.
doi: 10.1515/crll.1981.328.1. |
[8] |
M. Rordam, F. Larsen and N. J. Laustsen, An Introduction to K-Theory for C*-Algebras, Cambridge University Press, 2000.
![]() |
[9] |
M. Rosenkranz,
A new symbolic method for solving linear two-point boundary value problems on the level of operators, J. Symb. Comput, 39 (2005), 171-199.
doi: 10.1016/j.jsc.2004.09.004. |
[10] |
M. Tenenbaum and H. Pollard, Ordinary Differential Equations, Dover Publications Inc., 2012. Google Scholar |
[11] |
H. S. Yin,
A simple proof of the classification of rational rotation C*-algebras, P. Am. Math. Soc., 98 (1986), 469-470.
doi: 10.2307/2046204. |

[1] |
Kung-Ching Chang, Xuefeng Wang, Xie Wu. On the spectral theory of positive operators and PDE applications. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3171-3200. doi: 10.3934/dcds.2020054 |
[2] |
Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020108 |
[3] |
Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079 |
[4] |
Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093 |
[5] |
Hongliang Chang, Yin Chen, Runxuan Zhang. A generalization on derivations of Lie algebras. Electronic Research Archive, , () : -. doi: 10.3934/era.2020124 |
[6] |
Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, 2021, 29 (1) : 1681-1689. doi: 10.3934/era.2020086 |
[7] |
Mostafa Mbekhta. Representation and approximation of the polar factor of an operator on a Hilbert space. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020463 |
[8] |
Gökhan Mutlu. On the quotient quantum graph with respect to the regular representation. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020295 |
[9] |
Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel. Homogeneous darboux polynomials and generalising integrable ODE systems. Journal of Computational Dynamics, 2021, 8 (1) : 1-8. doi: 10.3934/jcd.2021001 |
[10] |
Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh. Asymptotic dynamics of hermitian Riccati difference equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020365 |
[11] |
Gabrielle Nornberg, Delia Schiera, Boyan Sirakov. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3857-3881. doi: 10.3934/dcds.2020128 |
[12] |
Alexandra Köthe, Anna Marciniak-Czochra, Izumi Takagi. Hysteresis-driven pattern formation in reaction-diffusion-ODE systems. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3595-3627. doi: 10.3934/dcds.2020170 |
[13] |
Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 |
[14] |
Matthieu Alfaro, Isabeau Birindelli. Evolution equations involving nonlinear truncated Laplacian operators. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3057-3073. doi: 10.3934/dcds.2020046 |
[15] |
Álvaro Castañeda, Pablo González, Gonzalo Robledo. Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020278 |
[16] |
Shanding Xu, Longjiang Qu, Xiwang Cao. Three classes of partitioned difference families and their optimal constant composition codes. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020120 |
[17] |
Jun Zhou. Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5581-5590. doi: 10.3934/cpaa.2020252 |
[18] |
Bing Sun, Liangyun Chen, Yan Cao. On the universal $ \alpha $-central extensions of the semi-direct product of Hom-preLie algebras. Electronic Research Archive, , () : -. doi: 10.3934/era.2021004 |
[19] |
Kengo Matsumoto. $ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. Electronic Research Archive, , () : -. doi: 10.3934/era.2021006 |
[20] |
Huiying Fan, Tao Ma. Parabolic equations involving Laguerre operators and weighted mixed-norm estimates. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5487-5508. doi: 10.3934/cpaa.2020249 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]