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Hopf, Eberhard (b. 1902 d. 1983)

Author ID: hopf.eberhard Recent zbMATH articles by "Hopf, Eberhard"
Published as: Hopf, E.; Hopf, Eberhard
Further Spellings: Hopf, Eberhard Frederich Ferdinand
External Links: MacTutor · MGP · Wikidata · GND · IdRef
Documents Indexed: 114 Publications since 1927, including 7 Books
1 Further Contribution
Biographic References: 5 Publications
Co-Authors: 12 Co-Authors with 8 Joint Publications
134 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

41 Publications have been cited 2,366 times in 2,247 Documents Cited by Year
The partial differential equation \(u_t+uu_x=\mu u_{xx}\). Zbl 0039.10403
Hopf, Eberhard
795
1950
Über die Anfangswertaufabe für die hydrodynamischen Grundgleichungen. Zbl 0042.10604
Hopf, Eberhard
507
1951
A remark on linear elliptic differential equations of second order. Zbl 0048.07802
Hopf, Eberhard
110
1952
Statistical hydromechanics and functional calculus. Zbl 0049.41704
Hopf, Eberhard
105
1952
A mathematical example displaying features of turbulence. Zbl 0031.32901
Hopf, Eberhard
95
1948
Closed surfaces without conjugate points. Zbl 0030.07901
Hopf, Eberhard
75
1948
Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems. Zbl 0063.02065
Hopf, Eberhard
73
1943
The general temporally discrete Markoff process. Zbl 0055.36705
Hopf, Eberhard
58
1954
Generalized solutions of non-linear equations of first order. Zbl 0168.35101
Hopf, E.
52
1965
Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung. Zbl 0002.34003
Hopf, Eberhard
50
1931
Über eine Klasse singulärer Integralgleichungen. Zbl 0003.30701
Wiener, N.; Hopf, E.
45
1931
Ergodic theory and the geodesic flow on surfaces of constant negative curvature. Zbl 0227.53003
Hopf, Eberhard
42
1971
An inequality for positive linear integral operators. Zbl 0115.32501
Hopf, E.
39
1963
Mathematical problems of radiative equilibrium. Zbl 0009.33004
Hopf, Eberhard
33
1934
Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Zbl 0024.08003
Hopf, Eberhard
29
1939
Ein allgemeiner Endlichkeitssatz der Hydrodynamik. Zbl 0024.13505
Hopf, Eberhard
27
1941
On S. Bernstein’s theorem on surfaces z(x,y) of nonpositive curvature. Zbl 0039.16901
Hopf, Eberhard
23
1950
On causality, statistics and probability. Zbl 0009.02703
Hopf, Eberhard
22
1934
Hamilton’s theory and generalized solutions of the Hamilton-Jacobi equation. Zbl 0178.11002
Conway, E. D.; Hopf, E.
20
1964
On the right weak solution of the Cauchy problem for a quasilinear equation of first order. Zbl 0188.16102
Hopf, E.
18
1969
On an inequality for minimal surfaces \(z=z(x,y)\). Zbl 0051.12601
Hopf, Eberhard
16
1953
Statistik der Lösungen geodätischer Probleme vom unstabilen Typus. 2. Zbl 0023.26801
Hopf, Eberhard
16
1940
Theory of measure and invariant integrals. Zbl 0004.26001
Hopf, Eberhard
14
1932
Fuchsian groups and ergodic theory. Zbl 0014.08303
Hopf, Eberhard
13
1936
Remarks on the preceding paper by D. Gilbarg. Zbl 0046.10404
Hopf, Eberhard
13
1952
Ergodic theory. (Ergodentheorie.) Zbl 0017.28301
Hopf, Eberhard
11
1937
On the ergodic theorem for positive linear operators. Zbl 0103.33801
Hopf, Eberhard
10
1960
On the time average theorem in dynamics. Zbl 0004.31101
Hopf, Eberhard
8
1932
Repeated branching through loss of stability. An example. Zbl 0073.41603
Hopf, Eberhard
8
1956
Selected works of Eberhard Hopf. With commentaries. Edited by Cathleen S. Morawetz, James B. Serrin and Yakov G. Sinai. Zbl 1011.01017
Hopf, Eberhard
7
2002
Complete transitivity and the ergodic principle. Zbl 0004.31201
Hopf, Eberhard
6
1932
Ergodentheorie. Zbl 0185.29001
Hopf, E.
5
1970
On Emden’s differential equation. Zbl 0002.10301
Hopf, Eberhard
4
1931
On certain special solutions of the \(\varPhi\)-equation of statistical hydrodynamics. Zbl 0053.45702
Hopf, E.; Titt, E. W.
4
1953
Proof of Gibbs’ hypothesis on the tendency toward statistical equilibrium. Zbl 0004.31202
Hopf, Eberhard
4
1932
Über einige Eigenschaften von Kurvenintegralen und über die Äquivalenz von indefiniten mit definiten Variationsproblemen. Zbl 0029.21603
Damköhler, W.; Hopf, E.
2
1947
Remarks on the functional-analytic approach to turbulence. Zbl 0122.44202
Hopf, E.
2
1962
Zur Kennzeichnung der Euklidischen Norm. Zbl 0088.08503
Hopf, Eberhard
2
1959
Five papers on the theory of probability. - Hopf, E.: Remarks on causality and probability. - Uhlenbeck, G. E.: The probability of position in a canonical ensemble. - Wiener, N.: Random functions. - Jessen, B.: Some analytical problems relating to probability. Bernstein, Felix: Principles of probability in natural science. Zbl 0011.12502
Hopf, E.; Uhlenbeck, G. E.; Wiener, N.; Jessen, B.; Bernstein, F.
1
1935
Über die Bedeutung der willkürlichen Funktionen für die Wahrscheinlichkeitstheorie. Zbl 0015.36004
Hopf, Eberhard
1
1936
Über eine Ungleichung der Ergodentheorie. Zbl 0031.15602
Hopf, Eberhard
1
1947
Selected works of Eberhard Hopf. With commentaries. Edited by Cathleen S. Morawetz, James B. Serrin and Yakov G. Sinai. Zbl 1011.01017
Hopf, Eberhard
7
2002
Ergodic theory and the geodesic flow on surfaces of constant negative curvature. Zbl 0227.53003
Hopf, Eberhard
42
1971
Ergodentheorie. Zbl 0185.29001
Hopf, E.
5
1970
On the right weak solution of the Cauchy problem for a quasilinear equation of first order. Zbl 0188.16102
Hopf, E.
18
1969
Generalized solutions of non-linear equations of first order. Zbl 0168.35101
Hopf, E.
52
1965
Hamilton’s theory and generalized solutions of the Hamilton-Jacobi equation. Zbl 0178.11002
Conway, E. D.; Hopf, E.
20
1964
An inequality for positive linear integral operators. Zbl 0115.32501
Hopf, E.
39
1963
Remarks on the functional-analytic approach to turbulence. Zbl 0122.44202
Hopf, E.
2
1962
On the ergodic theorem for positive linear operators. Zbl 0103.33801
Hopf, Eberhard
10
1960
Zur Kennzeichnung der Euklidischen Norm. Zbl 0088.08503
Hopf, Eberhard
2
1959
Repeated branching through loss of stability. An example. Zbl 0073.41603
Hopf, Eberhard
8
1956
The general temporally discrete Markoff process. Zbl 0055.36705
Hopf, Eberhard
58
1954
On an inequality for minimal surfaces \(z=z(x,y)\). Zbl 0051.12601
Hopf, Eberhard
16
1953
On certain special solutions of the \(\varPhi\)-equation of statistical hydrodynamics. Zbl 0053.45702
Hopf, E.; Titt, E. W.
4
1953
A remark on linear elliptic differential equations of second order. Zbl 0048.07802
Hopf, Eberhard
110
1952
Statistical hydromechanics and functional calculus. Zbl 0049.41704
Hopf, Eberhard
105
1952
Remarks on the preceding paper by D. Gilbarg. Zbl 0046.10404
Hopf, Eberhard
13
1952
Über die Anfangswertaufabe für die hydrodynamischen Grundgleichungen. Zbl 0042.10604
Hopf, Eberhard
507
1951
The partial differential equation \(u_t+uu_x=\mu u_{xx}\). Zbl 0039.10403
Hopf, Eberhard
795
1950
On S. Bernstein’s theorem on surfaces z(x,y) of nonpositive curvature. Zbl 0039.16901
Hopf, Eberhard
23
1950
A mathematical example displaying features of turbulence. Zbl 0031.32901
Hopf, Eberhard
95
1948
Closed surfaces without conjugate points. Zbl 0030.07901
Hopf, Eberhard
75
1948
Über einige Eigenschaften von Kurvenintegralen und über die Äquivalenz von indefiniten mit definiten Variationsproblemen. Zbl 0029.21603
Damköhler, W.; Hopf, E.
2
1947
Über eine Ungleichung der Ergodentheorie. Zbl 0031.15602
Hopf, Eberhard
1
1947
Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems. Zbl 0063.02065
Hopf, Eberhard
73
1943
Ein allgemeiner Endlichkeitssatz der Hydrodynamik. Zbl 0024.13505
Hopf, Eberhard
27
1941
Statistik der Lösungen geodätischer Probleme vom unstabilen Typus. 2. Zbl 0023.26801
Hopf, Eberhard
16
1940
Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Zbl 0024.08003
Hopf, Eberhard
29
1939
Ergodic theory. (Ergodentheorie.) Zbl 0017.28301
Hopf, Eberhard
11
1937
Fuchsian groups and ergodic theory. Zbl 0014.08303
Hopf, Eberhard
13
1936
Über die Bedeutung der willkürlichen Funktionen für die Wahrscheinlichkeitstheorie. Zbl 0015.36004
Hopf, Eberhard
1
1936
Five papers on the theory of probability. - Hopf, E.: Remarks on causality and probability. - Uhlenbeck, G. E.: The probability of position in a canonical ensemble. - Wiener, N.: Random functions. - Jessen, B.: Some analytical problems relating to probability. Bernstein, Felix: Principles of probability in natural science. Zbl 0011.12502
Hopf, E.; Uhlenbeck, G. E.; Wiener, N.; Jessen, B.; Bernstein, F.
1
1935
Mathematical problems of radiative equilibrium. Zbl 0009.33004
Hopf, Eberhard
33
1934
On causality, statistics and probability. Zbl 0009.02703
Hopf, Eberhard
22
1934
Theory of measure and invariant integrals. Zbl 0004.26001
Hopf, Eberhard
14
1932
On the time average theorem in dynamics. Zbl 0004.31101
Hopf, Eberhard
8
1932
Complete transitivity and the ergodic principle. Zbl 0004.31201
Hopf, Eberhard
6
1932
Proof of Gibbs’ hypothesis on the tendency toward statistical equilibrium. Zbl 0004.31202
Hopf, Eberhard
4
1932
Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung. Zbl 0002.34003
Hopf, Eberhard
50
1931
Über eine Klasse singulärer Integralgleichungen. Zbl 0003.30701
Wiener, N.; Hopf, E.
45
1931
On Emden’s differential equation. Zbl 0002.10301
Hopf, Eberhard
4
1931
all top 5

Cited by 2,765 Authors

31 Zhang, Zujin
16 Kudryashov, Nikolaĭ Alekseevich
15 Gala, Sadek
13 Farwig, Reinhard
12 Foiaș, Ciprian
12 Zhou, Yong
11 Joseph, Kayyunnapara Thomas
11 Temam, Roger Meyer
10 Awasthi, Ashish
10 Philippin, Gérard A.
10 Tsai, Tai-Peng
10 Yang, Xinguang
9 Kang, Kyungkeun
9 Sahoo, Manas Ranjan
8 Berselli, Luigi Carlo
8 Fang, Daoyuan
8 Galdi, Giovanni Paolo
8 Payne, Lawrence Edward
8 Serrin, James
8 Sinaĭ, Yakov Grigor’evich
8 Sophocleous, Christodoulos
8 Zhang, Ting
7 Beirão da Veiga, Hugo
7 Darbon, Jerome
7 Robinson, James Cooper
7 Shinbrot, Marvin
7 Vasseur, Alexis F.
7 Verma, Amit Kumar
7 Verma, Lajja
7 Yang, Jiaqi
6 Choe, Hi Jun
6 Cvitanović, Predrag
6 Dağ, İdris
6 Enache, Cristian
6 Gowda, G. D. Veerappa
6 Kadalbajoo, Mohan K.
6 Kerswell, Richard Rodney
6 Khenkin, Gennadiĭ Markovich
6 Kutluay, Selcuk
6 Leonenko, Nikolai N.
6 Lions, Jacques-Louis
6 Liu, Qiao
6 Liu, Tai-Ping
6 Maremonti, Paolo
6 Nitsche, Johannes Carl Christian
6 Ruggiero, Rafael Oswaldo
6 Sharma, Basant Lal
6 Šverák, Vladimír
6 Wang, Yuzhu
5 Bialy, Misha
5 Bradshaw, Zachary
5 Broadbridge, Philip
5 Brunton, Steven L.
5 Bulíček, Miroslav
5 Carillo, Sandra
5 Chae, Dongho
5 Chen, Hui
5 Cuesta Romero, Carlota Maria
5 Esen, Alaattin
5 Fan, Jishan
5 Finn, Robert Samuel
5 Fleming, Wendell Helms
5 Fukuda, Ikki
5 Guo, Zhengguang
5 He, Cheng
5 Heinz, Erhard
5 Heywood, John G.
5 Huang, Feimin
5 Innami, Nobuhiro
5 Kim, Jaemyoung
5 Kozono, Hideo
5 Ladyzhenskaya, Ol’ga Aleksandrovna
5 Mayil Vaganan, B.
5 Ozis, Turgut
5 Qian, Chenyin
5 Sinelshchikov, Dmitry I.
5 Sohr, Hermann
5 Sperb, Rene P.
5 Tarkhanov, Nikolai N.
5 Wang, Yanqing
4 Aaronson, Jon
4 Benameur, Jamel
4 Boritchev, Alexandre
4 Broer, Henk W.
4 Bunimovich, Leonid Abramovich
4 Büyükaşık, Şirin A.
4 Caginalp, Carey
4 Chacon, Rafael V. S.
4 Chen, Qionglei
4 Chung, Jaywan
4 Drivas, Theodore Dimitrios
4 Dunlap, Alexander
4 Engu, Satyanarayana
4 Erber, Thomas
4 Giga, Yoshikazu
4 Hajian, Arshag B.
4 Inoue, Atsushi
4 Ito, Yuji
4 Kamynin, Leonid Ivanovich
4 Knieper, Gerhard
...and 2,665 more Authors
all top 5

Cited in 446 Serials

92 Journal of Mathematical Analysis and Applications
71 Journal of Differential Equations
70 Archive for Rational Mechanics and Analysis
55 Applied Mathematics and Computation
40 Communications in Mathematical Physics
40 Journal of Mathematical Physics
38 Journal of Fluid Mechanics
32 Journal of Computational Physics
31 ZAMP. Zeitschrift für angewandte Mathematik und Physik
31 Proceedings of the American Mathematical Society
30 Mathematical Methods in the Applied Sciences
29 Mathematische Annalen
29 Nonlinear Analysis. Theory, Methods & Applications
28 Transactions of the American Mathematical Society
27 Physica D
27 Journal of Mathematical Fluid Mechanics
25 Mathematische Zeitschrift
25 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
24 Bulletin of the American Mathematical Society
22 Journal of Computational and Applied Mathematics
21 Computers & Mathematics with Applications
20 Journal of Mathematical Sciences (New York)
20 Discrete and Continuous Dynamical Systems
18 Ergodic Theory and Dynamical Systems
18 Communications in Nonlinear Science and Numerical Simulation
17 Physics Letters. A
17 Applied Mathematics Letters
16 Journal of Statistical Physics
16 Chaos, Solitons and Fractals
16 Acta Applicandae Mathematicae
15 Advances in Mathematics
14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
14 Communications in Partial Differential Equations
13 Applicable Analysis
13 Journal of Soviet Mathematics
13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
13 Stochastic Processes and their Applications
13 Nonlinear Analysis. Real World Applications
12 Israel Journal of Mathematics
12 Journal d’Analyse Mathématique
12 Mathematical Notes
12 Annali di Matematica Pura ed Applicata. Serie Quarta
12 Archiv der Mathematik
12 Numerical Methods for Partial Differential Equations
11 Journal of Engineering Mathematics
11 Wave Motion
11 Journal of Functional Analysis
11 Rendiconti del Seminario Matematico della Università di Padova
11 Calculus of Variations and Partial Differential Equations
11 Chaos
10 Nonlinearity
10 Physica A
10 Theoretical and Mathematical Physics
10 Numerische Mathematik
10 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
9 Computer Methods in Applied Mechanics and Engineering
9 Mathematics of Computation
9 Tôhoku Mathematical Journal. Second Series
9 Journal of Scientific Computing
9 Bulletin of the American Mathematical Society. New Series
8 Communications on Pure and Applied Mathematics
8 Inventiones Mathematicae
8 Studies in Applied Mathematics
8 Acta Mathematicae Applicatae Sinica. English Series
8 Mathematical and Computer Modelling
8 Journal de Mathématiques Pures et Appliquées. Neuvième Série
8 PMM, Journal of Applied Mathematics and Mechanics
7 Computers and Fluids
7 International Journal of Engineering Science
7 Annales de l’Institut Fourier
7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
7 Mathematische Nachrichten
7 Proceedings of the Japan Academy. Series A
7 Applications of Mathematics
7 Linear Algebra and its Applications
7 SIAM Journal on Mathematical Analysis
7 Journal of Nonlinear Science
7 Abstract and Applied Analysis
7 Annals of Mathematics. Second Series
7 Journal of Hyperbolic Differential Equations
6 Astrophysics and Space Science
6 Physics Reports
6 Duke Mathematical Journal
6 Manuscripta Mathematica
6 Monatshefte für Mathematik
6 Applied Numerical Mathematics
6 The Journal of Geometric Analysis
6 International Journal of Computer Mathematics
6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Mathematical Problems in Engineering
6 Communications on Pure and Applied Analysis
6 Boundary Value Problems
6 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
6 International Journal of Applied and Computational Mathematics
5 Indian Journal of Pure & Applied Mathematics
5 Transport Theory and Statistical Physics
5 Acta Mathematica
5 Applied Mathematics and Optimization
5 Bulletin de la Société Mathématique de France
...and 346 more Serials
all top 5

Cited in 58 Fields

1,315 Partial differential equations (35-XX)
730 Fluid mechanics (76-XX)
278 Numerical analysis (65-XX)
276 Dynamical systems and ergodic theory (37-XX)
144 Probability theory and stochastic processes (60-XX)
126 Differential geometry (53-XX)
115 Ordinary differential equations (34-XX)
93 Operator theory (47-XX)
62 Calculus of variations and optimal control; optimization (49-XX)
59 Statistical mechanics, structure of matter (82-XX)
54 Systems theory; control (93-XX)
53 Global analysis, analysis on manifolds (58-XX)
52 Measure and integration (28-XX)
48 Integral equations (45-XX)
43 Mechanics of deformable solids (74-XX)
35 Functional analysis (46-XX)
33 Biology and other natural sciences (92-XX)
30 Mechanics of particles and systems (70-XX)
26 Functions of a complex variable (30-XX)
26 Quantum theory (81-XX)
25 Computer science (68-XX)
19 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
17 Harmonic analysis on Euclidean spaces (42-XX)
15 History and biography (01-XX)
15 Group theory and generalizations (20-XX)
14 Linear and multilinear algebra; matrix theory (15-XX)
14 Topological groups, Lie groups (22-XX)
14 Potential theory (31-XX)
14 Classical thermodynamics, heat transfer (80-XX)
12 Real functions (26-XX)
12 Optics, electromagnetic theory (78-XX)
12 Astronomy and astrophysics (85-XX)
11 Manifolds and cell complexes (57-XX)
11 Operations research, mathematical programming (90-XX)
10 Number theory (11-XX)
10 Several complex variables and analytic spaces (32-XX)
10 Statistics (62-XX)
10 Geophysics (86-XX)
8 Approximations and expansions (41-XX)
8 Relativity and gravitational theory (83-XX)
7 Difference and functional equations (39-XX)
7 Integral transforms, operational calculus (44-XX)
6 General and overarching topics; collections (00-XX)
6 General topology (54-XX)
5 Algebraic geometry (14-XX)
5 Special functions (33-XX)
5 Abstract harmonic analysis (43-XX)
5 Information and communication theory, circuits (94-XX)
4 Geometry (51-XX)
3 Mathematical logic and foundations (03-XX)
2 Combinatorics (05-XX)
2 Convex and discrete geometry (52-XX)
2 Algebraic topology (55-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)
1 Nonassociative rings and algebras (17-XX)
1 Category theory; homological algebra (18-XX)
1 Mathematics education (97-XX)

Citations by Year

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