Lehrstuhl Mathematische Physik

Ausgewählte Veröffentlichungen

• Monographien

• Dissertationen und Habilitationen

• Artikel in Zeitschriften und Proceedings

• Preprints etc.

B. Carl, I. Stephani:  Entropy, compactness and the approximation of operators. Cambridge Tracts in Mathematics 98, Cambridge University Press, 1990.

R. Oloff:  Geometrie der Raumzeit - Eine mathematische Einführung in die Relativitätstheorie. Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 1999.

• H. Aden:  Elementary Operators and Solutions of the Korteweg-deVries Equations. Dissertationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 1996.
• C. Schiebold:  Funktionalanalytische Methoden bei der Behandlung von Solitonengleichungen. Dissertationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 1996.
• C. Richter:  Zerlegungen und Überdeckungen von Körpern. Dissertationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 1998.
• H. Blohm:  On the Solution of Nonlinear Evolution Equations and Corresponding Cauchy Problems by Trace Methods. Dissertationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 2000.
• I. Steinwart:  Entropy of  $C(K)$-valued operators and some applications. Dissertationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 2000.  [Abstract ...]
• C. Richter: Entropy and the approximation of functions on compact metric and topological spaces. Habilitationsschrift, Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, 2001.

Auswahl bis 1995

• B. Carl:  Absolut $(p,1)$-summierende Operatoren von $l_u$ nach $l_v$. Math. Nachr. 63, 353-360, 1974.
• B. Carl, A. Pietsch:  Some contributions to the theory of s-numbers. Commentationes Mathematicae 1977/78.
• B. Carl, B. Maurey, J. Puhl:  Grenzordnungen von absolut $(r,p)$-summierenden Operatoren. Math. Nachr. 82, 128-205, 1978.
• B. Carl:  Inequalities between $(p,q)$-summing norms. Studia Math. 69, 143-148, 1980.
• B. Carl, H. Triebel:  Inequalities between eigenvalues, entropy numbers, and related quantities of compact operators in Banach spaces. Math. Ann. 251, 129-133, 1980.
• B. Carl:  Entropy numbers, s-numbers, and eigenvalue problems. J. Funct. Anal. 41, 290-306, 1981.
• B. Carl:  Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems. Proc. Roy. Soc. Edinb. 90A, 63-70, 1981.
• B. Carl:  Entropy numbers of diagonal operators with an application to eigenvalue problems. J. Approx. Theory 32, 135-150, 1981.
• B. Carl:  On a characterization of operators from $l_q$ into a Banach space of type $p$ with some applications to eigenvalue problems. J. Funct. Anal. 48, 394-407, 1982.
• B. Carl:  Entropy numbers of $r$-nuclear operators between $L_p$-spaces. Studia Math. 77, 155-162, 1983.
• B. Carl, T. Kühn:  Entropy and eigenvalues of certain integral operators. Math. Ann. 268, 127-136, 1984.
• B. Carl, I. Stephani:  Estimating compactness properties of operators by the aid of generalized entropy numbers. J. Reine Angew. Math. 350, 1984, 117-136.
• B. Carl:  Inequalities of Bernstein-Jackson type and the degree of compactness of operators in Banach spaces. Ann. Inst. Fourier 35, 79-118, 1985.
• B. Carl, T. Kühn:  Local entropy moduli and eigenvalues of operators in Banach spaces. Revista Mat. Iberoamericana 1, 127-148, 1985.
• B. Carl, A. Pajor:  Gelfand numbers of operators with values in Hilbert spaces. Inventiones Math. 94 (3), 479-504, 1988.
• B. Carl, S. Heinrich, T. Kühn:  s-Numbers of integral operators with Hölder continuous kernels over metric compacta. J. Funct. Anal. 81 (1), 54-73,  1988.
• B. Carl, E. Makai:  New covering numbers and spectral properties of operators in Banach spaces. Hungarian Academy of Sciences Analysis Math. 17, 183-209, 1991.
• B. Carl, A. Heß:  Covering numbers of operators in Banach spaces. J. Approx. Theory 65, 121-139, 1991.
• B. Carl, A. Defant:  An inequality between the $p$- and $(p,1)$-summing norm of finite rank operators from $C(K)$-spaces. Israel Journal of Math. 74, 323-335, 1991.
• B. Carl, A. Defant:  Tensor products, entropy estimates, and Grothendieck type inequalities of operators in $L_p$-spaces. Transaction AMS 331 (1), 55-76, 1992.

• B. Carl, H. Aden:  On realizations of solutions of the KdV equation by determinants on operator ideals. J. Math. Phys. 37 (4), 1833-1857, 1996.
• C. Richter, I. Stephani:  Entropy and the approximation of bounded functions and operators. Arch. Math. 67, 478-492, 1996.  [Abstract ...]

• W. Börner, C. Richter:  Entropy, capacity and arrangements on the cube. Beiträge Algebra Geom. 38, 227-232, 1997.  [Abstract ...]
• B. Carl, A. Defant:  Asymptotic estimates for approximation quantities of tensor product idendities. J. Approx. Theory 88, 228-256, 1997.
• B. Carl:  Metric entropy of convex hulls in Hilbert spaces. Bull. London Math. Soc. 29, 452-458, 1997.
• C. Richter:  Chains of controllable partitions of the m-dimensional cube. Arch. Math. 68, 331-339, 1997.  [Abstract ...]

• E. Dietzel, H. Toparkus:  The explicit solution of the characteristical initial value problem for canonical hyperbolic systems by means of the two-dimensional Laplace transform. Integral Transform. Spec. Funct. 7, 225-236, 1998.
• C. Schiebold:  An operator theoretic approach to the Toda lattice equation. Phys. D 122, 37-61, 1998.
• I. Stephani:  Embedding maps of generalized Hölder spaces - Entropy and approximation. Rend. Circ. Mat. Palermo (2) Suppl. 52, 793-804, 1998.

• H. Blohm:  Solution of a discrete inverse scattering problem and of the Cauchy problem of a class of discrete evolution equations. J. Math. Phys. 40, 4374-4392, 1999.  [Abstract ...]
• B. Carl, C. Schiebold:  Nonlinear equations in soliton physics and operator ideals. Nonlinearity 12, 333-364, 1999.
• C. Richter:  Entropy, approximation quantities and the asymptotics of the modulus of continuity. Math. Nachr. 198, 179-188, 1999.  [Abstract ...]
• C. Richter:  A chain of controllable partitions of unity on the cube and the approximation of Hölder continuous functions. Illinois J. Math. 43, 159-191, 1999.  [Abstract ...]

• B. Carl, D.E. Edmunds:  Coverings of convex sets and volume inequalities. Discrete Comput. Geom. 23, 51-71, 2000.
• I. Steinwart:  Entropy of C(K)-valued operators. J. Approx. Theory 103, 302-328, 2000.

• B. Carl:  Metric entropy conditions for operators, Schatten classes and eigenvalue problems. Symposium "Numbers, Information and Complexity", Kluwer.
• B. Carl, A. Defant:  An elementary approach to an eigenvalue estimate for matrices. Positivity.
• B. Carl, S.-Z. Huang:  On realizations of solutions of the KdV equation by the $C_0$-semigroup method. Amer. Journal of Mathematics.
• B. Carl, I. Kyrezi, A. Pajor:  Metric entropy of convex hulls in Banach spaces. J. London Math. Soc.
• B. Carl, C. Schiebold:  Ein direkter Ansatz zur Untersuchung von Solitonengleichungen. Jahresber. Deutsch. Math.-Verein.
• J. Creutzig, I. Steinwart:  Metric entropy of convex hulls in type p spaces - The critical case. Proc. Amer. Math. Soc.  [.ps-File]
• C. Richter:  Representing cliquish functions as quasiuniform limits of quasicontinuous functions. Real Anal. Exchange.  [Abstract ...]
• C. Richter:  n-Term approximation by controllable step functions. Math. Nachr.  [Abstract ...]

1996

• C. Richter:  Entropy, approximation and the geometry of the cube. Preprint, Jena, 1996.  [Abstract ...]

• I. Bartels:  Gewichtete Normungleichungen für Operatoren zwischen Räumen Bochner-integrierbarer Funktionen. Diplomarbeit, Oldenburg, 1997.
• C. Richter:  C(X)-spaces consisting of polynomials only. Preprint, Jena, 1997.

• C. Richter:  Metrics on compact spaces compatible with entropy properties. Preprint, Jena, 1998.  [Abstract ...]

• H. Blohm:  Solution of inverse scattering problems and non-linear equations by trace methods. (submitted)
• B. Carl, D.E. Edmunds:  Entropy of $C(X)$-valued operators and diverse applications. (submitted)
• C. Richter:  Linear combinations of partitions of unity with restricted supports. Preprint, Jena, 1999.  [Abstract ...]
• C. Richter, I. Stephani:  Characterizing compact metrizable spaces among completely regular spaces. Preprint, Jena, 1999.  [Abstract ...]
• C. Schiebold:  Solitons of the sine-Gordon equation coming in clusters. Preprint, Jena, 1999.
• I. Steinwart:  Some estimates for the entropy numbers of convex hulls with finitely many extreme points. Preprint, Jena, 1999.  [.ps-File]

• C. Richter, I. Stephani:  Local and global properties of quasi-continuous and cliquish functions. Preprint, Jena, 2000.  [Abstract ...]

• I. Steinwart:  On the influence of the kernel on the generalization ability of support vector machines. Preprint, Jena, 2001.  [Abstract ...]