## Hilger, Stefan

Compute Distance To:
 Author ID: hilger.stefan Published as: Hilger, Stefan; Hilger, S.
 Documents Indexed: 28 Publications since 1988, including 1 Book 1 Contribution as Editor Reviewing Activity: 106 Reviews Co-Authors: 14 Co-Authors with 17 Joint Publications 803 Co-Co-Authors
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### Co-Authors

 12 single-authored 4 Filipuk, Galina V. 4 Kloeden, Peter Eris 3 Aulbach, Bernd 2 Eloe, Paul W. 2 Garay, Barnabas M. 1 Colonius, Fritz 1 Došlý, Ondřej 1 Erbe, Lynn Harry 1 Esty, Norah Catherine 1 Graef, John R. 1 Pinelas, Sandra 1 Schinas, Christos J. 1 Sheng, Qin 1 Siegmund, Stefan
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### Serials

 6 Journal of Difference Equations and Applications 3 Results in Mathematics 2 Journal of Computational and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 Journal of Functional Analysis 1 Journal of Pure and Applied Algebra 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Dynamic Systems and Applications 1 Automation and Remote Control 1 Journal of the Australian Mathematical Society. Series A 1 Differential Equations and Dynamical Systems 1 Differential Equations and Applications 1 Springer Proceedings in Mathematics & Statistics 1 Nonlinear Analysis. Theory, Methods & Applications
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### Fields

 20 Difference and functional equations (39-XX) 15 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Quantum theory (81-XX) 3 Real functions (26-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Numerical analysis (65-XX) 3 Systems theory; control (93-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Special functions (33-XX) 2 Partial differential equations (35-XX) 2 General topology (54-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX)

### Citations contained in zbMATH Open

24 Publications have been cited 1,524 times in 1,177 Documents Cited by Year
Analysis on measure chains - a unified approach to continuous and discrete calculus. Zbl 0722.39001
Hilger, Stefan
1990
Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Zbl 0695.34001
Hilger, Stefan
1988
Sturmian theory on measure chains. Zbl 0868.39007
Erbe, Lynn; Hilger, Stefan
1993
Linear dynamic processes with inhomogeneous time scale. Zbl 0719.34088
Aulbach, Bernd; Hilger, Stefan
1990
Differential and difference calculus – unified! Zbl 0927.39002
Hilger, Stefan
1997
A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales. Zbl 1009.34033
Došlý, Ondřej; Hilger, Stefan
2002
Special functions, Laplace and Fourier transform on measure chains. Zbl 0943.39006
Hilger, Stefan
1999
A unified approach to continuous and discrete dynamics. Zbl 0723.34030
Aulbach, B.; Hilger, S.
1990
A unified approach to continuous and discrete dynamics. Zbl 0713.34050
Aulbach, B.; Hilger, S.
1990
Generalized theorem of Hartman-Grobman on measure chains. Zbl 0853.39007
Hilger, Stefan
1996
The category of ladders. Zbl 1193.81028
Hilger, Stefan
2010
Matrix Lie theory and measure chains. Zbl 1160.22307
Hilger, Stefan
2002
Embeddability of time scale dynamics in ODE dynamics. Zbl 1042.34503
Garay, Barnabas M.; Hilger, Stefan
2001
A qualitative analysis on nonconstant graininess of the adaptive grids via time scales. Zbl 1135.65030
Eloe, P. W.; Hilger, S.; Sheng, Q.
2006
Smoothness of invariant manifolds. Zbl 0762.93041
Hilger, Stefan
1992
Factorization of $$(q, h)$$-difference operators – an algebraic approach. Zbl 1298.39010
Hilger, Stefan; Filipuk, Galina
2014
An application of calculus on measure chains to Fourier theory and Heisenberg’s uncertainty principle. Zbl 1006.43002
Hilger, Stefan
2002
Continuous dependence in time scale dynamics. Zbl 1065.39030
Garay, Barnabas M.; Hilger, Stefan; Kloeden, Peter E.
2004
Algebra embedding of $$U_{q}(sl(2))$$ into the tensor product of two $$(q,h)$$-Weyl algebras. Zbl 1347.16026
Filipuk, Galina; Hilger, Stefan
2016
The discrete and periodic heat and harmonic oscillator equation. Zbl 1132.39013
Hilger, Stefan
2007
Linear graininess time scales and ladder operators of orthogonal polynomials. Zbl 1284.26038
Filipuk, Galina; Hilger, Stefan
2013
Convergence of time scales under the Fell topology. Zbl 1185.34142
Esty, Norah; Hilger, Stefan
2009
The harmonic oscillator – an extension via measure chains. Zbl 1117.39321
Hilger, Stefan
2005
Comparative time graininess and asymptotic stability of dynamical systems. Zbl 0855.93072
Hilger, S.; Kloeden, P. E.
1994
Algebra embedding of $$U_{q}(sl(2))$$ into the tensor product of two $$(q,h)$$-Weyl algebras. Zbl 1347.16026
Filipuk, Galina; Hilger, Stefan
2016
Factorization of $$(q, h)$$-difference operators – an algebraic approach. Zbl 1298.39010
Hilger, Stefan; Filipuk, Galina
2014
Linear graininess time scales and ladder operators of orthogonal polynomials. Zbl 1284.26038
Filipuk, Galina; Hilger, Stefan
2013
The category of ladders. Zbl 1193.81028
Hilger, Stefan
2010
Convergence of time scales under the Fell topology. Zbl 1185.34142
Esty, Norah; Hilger, Stefan
2009
The discrete and periodic heat and harmonic oscillator equation. Zbl 1132.39013
Hilger, Stefan
2007
A qualitative analysis on nonconstant graininess of the adaptive grids via time scales. Zbl 1135.65030
Eloe, P. W.; Hilger, S.; Sheng, Q.
2006
The harmonic oscillator – an extension via measure chains. Zbl 1117.39321
Hilger, Stefan
2005
Continuous dependence in time scale dynamics. Zbl 1065.39030
Garay, Barnabas M.; Hilger, Stefan; Kloeden, Peter E.
2004
A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales. Zbl 1009.34033
Došlý, Ondřej; Hilger, Stefan
2002
Matrix Lie theory and measure chains. Zbl 1160.22307
Hilger, Stefan
2002
An application of calculus on measure chains to Fourier theory and Heisenberg’s uncertainty principle. Zbl 1006.43002
Hilger, Stefan
2002
Embeddability of time scale dynamics in ODE dynamics. Zbl 1042.34503
Garay, Barnabas M.; Hilger, Stefan
2001
Special functions, Laplace and Fourier transform on measure chains. Zbl 0943.39006
Hilger, Stefan
1999
Differential and difference calculus – unified! Zbl 0927.39002
Hilger, Stefan
1997
Generalized theorem of Hartman-Grobman on measure chains. Zbl 0853.39007
Hilger, Stefan
1996
Comparative time graininess and asymptotic stability of dynamical systems. Zbl 0855.93072
Hilger, S.; Kloeden, P. E.
1994
Sturmian theory on measure chains. Zbl 0868.39007
Erbe, Lynn; Hilger, Stefan
1993
Smoothness of invariant manifolds. Zbl 0762.93041
Hilger, Stefan
1992
Analysis on measure chains - a unified approach to continuous and discrete calculus. Zbl 0722.39001
Hilger, Stefan
1990
Linear dynamic processes with inhomogeneous time scale. Zbl 0719.34088
Aulbach, Bernd; Hilger, Stefan
1990
A unified approach to continuous and discrete dynamics. Zbl 0723.34030
Aulbach, B.; Hilger, S.
1990
A unified approach to continuous and discrete dynamics. Zbl 0713.34050
Aulbach, B.; Hilger, S.
1990
Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Zbl 0695.34001
Hilger, Stefan
1988
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### Cited by 983 Authors

 54 Bohner, Martin J. 49 Agarwal, Ravi P. 30 Li, Tongxing 29 Saker, Samir H. 27 Anderson, Douglas Robert 27 O’Regan, Donal 25 Peterson, Allan C. 23 Erbe, Lynn Harry 22 Šimon Hilscher, Roman 21 Eldeeb, Ahmed Abdel-Moneim 21 Han, Zhenlai 21 Li, Yongkun 20 Hassan, Taher S. 19 Sun, Shurong 18 Li, Wan-Tong 18 Qiu, Yangcong 16 Grace, Said Rezk 16 Sun, Hongrui 16 Torres, Delfim Fernando Marado 16 Wang, Chao 15 Hilger, Stefan 14 Sun, Jianping 13 Abbas, Syed 13 Guseinov, Gusein Sh. 13 Kaymakçalan, Billur 13 Zhang, Chenghui 12 Davis, John M. 12 Wang, Qiru 12 Zada, Akbar 11 Sun, Taixiang 11 Zeidan, Vera Michel 10 Henderson, Johnny Lee 10 Li, Weinian 10 Malinowska, Agnieszka Barbara 10 Meng, Fanwei 10 Oganesyan, Gro R. 10 Su, Youhui 9 Ardjouni, Abdelouaheb 9 Djoudi, Ahcene 9 Dogan, Abdulkadir 9 Feng, Qinghua 9 Karpuz, Başak 9 Prasad, Kapula Rajendra 9 Shah, Syed Omar 9 Tuna, Hüseyin 9 Wang, Dabin 9 Zhang, Jimin 8 Ge, Weigao 8 Kong, Qingkai 8 Malik, Muslim 8 Martins, Natália F. 8 Nguyen Huu Du 8 Pečarić, Josip 8 Slavík, Antonín 8 Stehlík, Petr 8 Xi, Hongjian 8 Zhang, Yi 7 Chyan, Chuan Jen 7 Defoort, Michael 7 Djemai, Mohamed 7 Eloe, Paul W. 7 Elsennary, Hamza A. 7 Fan, Meng 7 Guan, Wen 7 Hong, Shihuang 7 Khan, Zareen Abdulhameed 7 Liu, Haidong 7 Yang, Li 7 Yaslan Karaca, Ilkay 7 Yılmaz, Emrah Sercan 7 Zemánek, Petr 7 Zheng, Bin 6 Allahverdiev, Bilender Paşaoğlu 6 Bartosiewicz, Zbigniew 6 Diblík, Josef 6 Girejko, Ewa 6 Gravagne, Ian A. 6 Hamza, Alaa E. 6 Kong, Lingju 6 Koo, Namjip 6 Luo, Hua 6 Mesquita, Jaqueline Godoy 6 Negi, Shekhar Singh 6 Pachpatte, Deepak B. 6 Pötzsche, Christian 6 Rashid, Saima 6 Řehák, Pavel 6 Sheng, Qin 6 Tang, Shuhong 6 Tisdell, Christopher C. 6 Vítovec, Jiří 6 Xia, Yonghui 6 Zhang, Chao 5 Akın-Bohner, Elvan 5 Amster, Pablo 5 Aulbach, Bernd 5 Băleanu, Dumitru I. 5 Boukerrioua, Khaled 5 Chhatria, Gokula Nanda 5 Choi, Sungkyu ...and 883 more Authors
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### Cited in 207 Serials

 153 Advances in Difference Equations 75 Journal of Mathematical Analysis and Applications 60 Computers & Mathematics with Applications 53 Applied Mathematics and Computation 52 Abstract and Applied Analysis 50 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 40 Journal of Computational and Applied Mathematics 40 Journal of Difference Equations and Applications 39 Discrete Dynamics in Nature and Society 27 Journal of Inequalities and Applications 24 Mathematical and Computer Modelling 23 Journal of Applied Mathematics and Computing 21 Applied Mathematics Letters 16 Rocky Mountain Journal of Mathematics 13 Journal of Mathematical Physics 13 Journal of Applied Mathematics 12 Results in Mathematics 11 Differential Equations and Dynamical Systems 11 Qualitative Theory of Dynamical Systems 10 Mathematical Methods in the Applied Sciences 10 Turkish Journal of Mathematics 10 Boundary Value Problems 9 Journal of Differential Equations 9 Communications in Nonlinear Science and Numerical Simulation 9 Nonlinear Analysis. Hybrid Systems 9 Journal of Nonlinear Science and Applications 8 Acta Applicandae Mathematicae 8 Filomat 8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 7 Journal of Mathematical Sciences (New York) 7 Mediterranean Journal of Mathematics 7 Differential Equations and Applications 6 Nonlinear Analysis. Real World Applications 6 Kragujevac Journal of Mathematics 6 International Journal of Differential Equations 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 Journal of Function Spaces 5 Applicable Analysis 5 Computational and Applied Mathematics 5 Doklady Mathematics 5 Journal of Applied Analysis and Computation 4 International Journal of Control 4 Journal of the Franklin Institute 4 Mathematical Notes 4 Chaos, Solitons and Fractals 4 Mathematische Nachrichten 4 Proceedings of the American Mathematical Society 4 Acta Mathematicae Applicatae Sinica. English Series 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Integral Transforms and Special Functions 4 Arab Journal of Mathematical Sciences 4 Communications in Mathematical Analysis 4 Journal of Mathematical Inequalities 4 Advances in Mathematical Physics 4 Science China. Mathematics 3 Indian Journal of Pure & Applied Mathematics 3 Acta Mathematica Vietnamica 3 Journal of Optimization Theory and Applications 3 Mathematica Slovaca 3 Quaestiones Mathematicae 3 Systems & Control Letters 3 MCSS. Mathematics of Control, Signals, and Systems 3 Electronic Journal of Differential Equations (EJDE) 3 Fractals 3 Complexity 3 Mathematical Problems in Engineering 3 Journal of Dynamical Systems and Geometric Theories 3 Hacettepe Journal of Mathematics and Statistics 3 Electronic Journal of Mathematical Analysis and Applications EJMAA 3 Nonautonomous Dynamical Systems 3 AIMS Mathematics 2 Reports on Mathematical Physics 2 Ukrainian Mathematical Journal 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Demonstratio Mathematica 2 Hiroshima Mathematical Journal 2 Journal of Functional Analysis 2 Circuits, Systems, and Signal Processing 2 Applied Mathematics and Mechanics. (English Edition) 2 Stochastic Analysis and Applications 2 Communications in Statistics. Theory and Methods 2 International Applied Mechanics 2 Journal of the Egyptian Mathematical Society 2 Georgian Mathematical Journal 2 Journal of Applied Analysis 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Honam Mathematical Journal 2 Mathematical Inequalities & Applications 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Acta Mathematica Sinica. English Series 2 The ANZIAM Journal 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 2 Discrete and Continuous Dynamical Systems. Series B 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Foundations of Physics 2 Nonlinear Oscillations 2 Applications and Applied Mathematics 2 Applicable Analysis and Discrete Mathematics 2 Discrete and Continuous Dynamical Systems. Series S ...and 107 more Serials
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### Cited in 50 Fields

 866 Ordinary differential equations (34-XX) 375 Difference and functional equations (39-XX) 254 Real functions (26-XX) 116 Operator theory (47-XX) 72 Systems theory; control (93-XX) 60 Dynamical systems and ergodic theory (37-XX) 57 Biology and other natural sciences (92-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 41 Integral equations (45-XX) 27 Partial differential equations (35-XX) 23 Numerical analysis (65-XX) 14 Abstract harmonic analysis (43-XX) 14 Integral transforms, operational calculus (44-XX) 14 Mechanics of particles and systems (70-XX) 14 Quantum theory (81-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Functional analysis (46-XX) 12 Probability theory and stochastic processes (60-XX) 10 Operations research, mathematical programming (90-XX) 9 Sequences, series, summability (40-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Measure and integration (28-XX) 7 Special functions (33-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Differential geometry (53-XX) 6 Approximations and expansions (41-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Number theory (11-XX) 3 Associative rings and algebras (16-XX) 3 General topology (54-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 2 General and overarching topics; collections (00-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)