Bernd Carl

1.6k total citations
45 papers, 950 citations indexed

About

Bernd Carl is a scholar working on Mathematical Physics, Applied Mathematics and Statistics and Probability. According to data from OpenAlex, Bernd Carl has authored 45 papers receiving a total of 950 indexed citations (citations by other indexed papers that have themselves been cited), including 30 papers in Mathematical Physics, 27 papers in Applied Mathematics and 11 papers in Statistics and Probability. Recurrent topics in Bernd Carl's work include Advanced Banach Space Theory (18 papers), Advanced Harmonic Analysis Research (13 papers) and Approximation Theory and Sequence Spaces (11 papers). Bernd Carl is often cited by papers focused on Advanced Banach Space Theory (18 papers), Advanced Harmonic Analysis Research (13 papers) and Approximation Theory and Sequence Spaces (11 papers). Bernd Carl collaborates with scholars based in Germany, France and United Kingdom. Bernd Carl's co-authors include Irmtraud Stephani, Alain Pajor, Cornelia Schiebold, Hans Triebel, Andreas Defant, Aicke Hinrichs, Thomas Kühn, Stefan Heinrich, M. S. Ramanujan and D. E. Edmunds and has published in prestigious journals such as Transactions of the American Mathematical Society, Inventiones mathematicae and Journal of Mathematical Physics.

In The Last Decade

Bernd Carl

45 papers receiving 862 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Bernd Carl Germany	14	539	423	216	188	130	45	950
Y. Gordon Israel	16	486 0.9×	361 0.9×	237 1.1×	64 0.3×	19 0.1×	48	793
Kenneth B. Stolarsky United States	16	593 1.1×	198 0.5×	53 0.2×	239 1.3×	60 0.5×	75	1.2k
Z. Ciesielski Poland	14	399 0.7×	327 0.8×	100 0.5×	107 0.6×	34 0.3×	37	793
Carl Herz Canada	16	854 1.6×	789 1.9×	200 0.9×	67 0.4×	46 0.4×	36	1.3k
Hermann König Germany	15	638 1.2×	506 1.2×	180 0.8×	129 0.7×	18 0.1×	57	885
Anthony Carbery United Kingdom	21	1.1k 2.0×	650 1.5×	58 0.3×	112 0.6×	34 0.3×	82	1.3k
R. Creighton Buck United States	13	406 0.8×	271 0.6×	224 1.0×	144 0.8×	98 0.8×	47	1.0k
Franck Barthe France	16	495 0.9×	159 0.4×	193 0.9×	41 0.2×	105 0.8×	31	768
Pokman Cheung United Kingdom	4	700 1.3×	112 0.3×	206 1.0×	233 1.2×	134 1.0×	6	984
G. J. O. Jameson United Kingdom	12	319 0.6×	255 0.6×	137 0.6×	111 0.6×	45 0.3×	63	804

Countries citing papers authored by Bernd Carl

Since Specialization

Citations

This map shows the geographic impact of Bernd Carl's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Bernd Carl with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Bernd Carl more than expected).

Fields of papers citing papers by Bernd Carl

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Bernd Carl. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Bernd Carl. The network helps show where Bernd Carl may publish in the future.

Co-authorship network of co-authors of Bernd Carl

This figure shows the co-authorship network connecting the top 25 collaborators of Bernd Carl. A scholar is included among the top collaborators of Bernd Carl based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Bernd Carl. Bernd Carl is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

Carl, Bernd. (2008). On a Weyl inequality of operators in Banach spaces. Proceedings of the American Mathematical Society. 137(1). 155–159. 2 indexed citations

Carl, Bernd & D. E. Edmunds. (2000). Coverings of Convex Sets and Volume Inequalities. Discrete & Computational Geometry. 23(1). 51–71. 1 indexed citations

Carl, Bernd, et al.. (2000). On realizations of solutions of the KDV equation by the C 0 -semigroup method. American Journal of Mathematics. 122(2). 403–438. 7 indexed citations

Carl, Bernd & Andreas Defant. (2000). An Elementary Approach to an Eigenvalue Estimate for Matrices. Positivity. 4(2). 131–141. 3 indexed citations

Carl, Bernd & Cornelia Schiebold. (2000). Ein direkter Ansatz zur Untersuchung von Solitonengleichungen. 102(3). 102–148. 22 indexed citations

Carl, Bernd & Cornelia Schiebold. (1999). Nonlinear equations in soliton physics and operator ideals. Nonlinearity. 12(2). 333–364. 39 indexed citations

Carl, Bernd & Andreas Defant. (1997). Asymptotic Estimates for Approximation Quantities of Tensor Product Identities. Journal of Approximation Theory. 88(2). 228–256. 7 indexed citations

Carl, Bernd, et al.. (1996). On realizations of solutions of the KdV equation by determinants on operator ideals. Journal of Mathematical Physics. 37(4). 1833–1857. 38 indexed citations

Carl, Bernd & Andreas Defant. (1992). Tensor Products and Grothendieck Type Inequalities of Operators in L p - Spaces. Transactions of the American Mathematical Society. 331(1). 55–55. 7 indexed citations

10.

Carl, Bernd & Andreas Defant. (1992). Tensor products and Grothendieck type inequalities of operators in 𝐿_{𝑝}-spaces. Transactions of the American Mathematical Society. 331(1). 55–76. 11 indexed citations

11.

Carl, Bernd & Endre Makai. (1991). New covering numbers and spectral properties of operators in Banach spaces. Analysis Mathematica. 17(3). 183–209. 5 indexed citations

12.

Carl, Bernd, Stefan Heinrich, & Thomas Kühn. (1988). s-Numbers of integral operators with Hölder continuous kernels over metric compacta. Journal of Functional Analysis. 81(1). 54–73. 14 indexed citations

13.

Carl, Bernd. (1985). Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces. Annales de l’institut Fourier. 35(3). 79–118. 76 indexed citations

14.

Carl, Bernd. (1983). Entropy numbers of r-nuclear operators between $L_{p}$ spaces. Studia Mathematica. 77(2). 155–162. 1 indexed citations

15.

Carl, Bernd. (1982). On a characterization of operators from lq into a Banach space of type p with some applications to eigenvalue problems. Journal of Functional Analysis. 48(3). 394–407. 12 indexed citations

16.

Carl, Bernd. (1982). Inequalities between geometric quantities of operators in Banach spaces. Integral Equations and Operator Theory. 5(1). 759–773. 2 indexed citations

17.

Carl, Bernd. (1981). Entropy numbers, s-numbers, and eigenvalue problems. Journal of Functional Analysis. 41(3). 290–306. 134 indexed citations

18.

Carl, Bernd. (1981). Entropy numbers of diagonal operators with an application to eigenvalue problems. Journal of Approximation Theory. 32(2). 135–150. 28 indexed citations

19.

Carl, Bernd & Hans Triebel. (1980). Inequalities between eigenvalues, entropy numbers, and related quantities of compact operators in Banach spaces. Mathematische Annalen. 251(2). 129–133. 52 indexed citations

20.

Carl, Bernd, et al.. (1978). Grenzordnungen von absolut‐(r, p)‐summierenden Operatoren. Mathematische Nachrichten. 82(1). 205–218. 5 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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