Roger D. Nussbaum Explained

Roger David Nussbaum (born 29 January 1944, in Philadelphia)^[1] is an American mathematician, specializing in nonlinear functional analysis and differential equations.

Nussbaum graduated in 1965 with a bachelor's degree from Harvard University. He received his Ph.D. in 1969 from the University of Chicago with thesis The Fixed Point Index and Fixed Point Theorems for K-Set Contractions supervised by Felix Browder. At Rutgers University Nussbaum became in 1969 an assistant professor, in 1973 an associate professor, and in 1977 a full professor. He retired there as professor emeritus.^[2] He was elected in 2012 a Fellow of the American Mathematical Society.

Selected publications

Articles

• 10.1090/S0002-9904-1968-11988-3. The topological degree for noncompact nonlinear mappings in Banach spaces. 1968. Browder. Felix E.. Nussbaum. Roger D.. Bulletin of the American Mathematical Society. 74. 4. 671–677. free.
• 10.1090/S0002-9904-1969-12213-5. The fixed point index and asymptotic fixed point theorems for k -set-contractions. 1969. Nussbaum. Roger D.. Bulletin of the American Mathematical Society. 75. 3. 490–496. free.
• Nussbaum, Roger D.. 2. The radius of the essential spectrum. Duke Mathematical Journal. 37. 3. 1970. 473–478. 10.1215/S0012-7094-70-03759-2.
• 10.1090/S0002-9947-1970-0265967-9. Spectral mapping theorems and perturbation theorems for Browder's essential spectrum. 1970. Nussbaum. Roger D.. 2. Transactions of the American Mathematical Society. 150. 2. 445–455. free.
• Nussbaum. Roger D.. 2. The fixed point index for local condensing maps. Annali di Matematica Pura ed Applicata. 89. 1. 1971. 217–258. 0373-3114. 10.1007/BF02414948. 119544692 . free.
• 10.1090/S0002-9904-1971-12694-0. Some fixed point theorems. 1971. Nussbaum. Roger D.. 2. Bulletin of the American Mathematical Society. 77. 3. 360–366. free.
• 10.1090/S0002-9947-1972-0310719-6. Some asymptotic fixed point theorems. 1972. Nussbaum. Roger D.. 2. Transactions of the American Mathematical Society. 171. 349–375. free.
• 10.1090/S0002-9947-1978-0482913-0. A Hopf global bifurcation theorem for retarded functional differential equations. 1978. Nussbaum. Roger D.. 2. Transactions of the American Mathematical Society. 238. 139–164. free.
• Book: Nussbaum, Roger D.. 2. Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem. In: Fixed point theory. Lecture Notes in Mathematics. 309–330. Springer. Berlin; Heidelberg. 1981. 886. 10.1007/BFb0092191. 978-3-540-11152-8. https://link.springer.com/chapter/10.1007%2FBFb0092191.
• Book: De Figueiredo D.G.. Lions P.L.. Nussbaum R.D.. 2. 1982. A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations. In: Costa D. (ed.) Djairo G. de Figueiredo - Selected Papers. 133–155 . Springer. Cham, Switzerland. 10.1007/978-3-319-02856-9_11 . 978-3-319-02855-2 . https://doi.org/10.1007/978-3-319-02856-9_11. (over 600 citations)
• Nussbaum. Roger D.. 2. Some remarks on a conjecture in parameter adaptive control. Systems & Control Letters. 3. 5. 1983. 243–246. 0167-6911. 10.1016/0167-6911(83)90021-X. (over 1100 citations)
• 10.1090/S0002-9947-98-01998-9. Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators. 1998. Nussbaum. Roger D.. 2. Walsh. Bertram. Transactions of the American Mathematical Society. 350. 6. 2367–2391. free.
• 10.1090/S0002-9939-2010-10511-7. Inequivalent measures of noncompactness and the radius of the essential spectrum. 2011. Mallet-Paret. John. Nussbaum. Roger D.. 2. Proceedings of the American Mathematical Society. 139. 3. 917–930. free.
• 10.1090/S0002-9947-2011-05484-X. Positive operators and Hausdorff dimension of invariant sets. 2012. Nussbaum. Roger D.. 2. Priyadarshi. Amit. Verduyn Lunel. Sjoerd. Transactions of the American Mathematical Society. 364. 2. 1029–1066. free.
• 10.1090/S0002-9939-2013-11520-0. Continuity of the cone spectral radius. 2013. Lemmens. Bas. Nussbaum. Roger. 2. Proceedings of the American Mathematical Society. 141. 8. 2741–2754. free. 1107.4532.

Books

• with Bas Lemmens: Nonlinear Perron-Frobenius Theory, Cambridge Tracts in Mathematics, Cambridge University Press 2012
• with S. M. Verduyn-Lunel: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps, Memoirs AMS 1999
• with Heinz-Otto Peitgen: Special and Spurious Solutions of • x (t) =- \alpha f(x(t -1 )) , Memoirs AMS, 1984
• with Patrick Fitzpatrick, Jean Mawhin, Mario Martelli: Topological Methods for Ordinary Differential Equations, CIME Lectures, Montecacini Terme 1991, Lecture Notes in Mathematics 1537, Springer Verlag 1993
• Hilbert's projective metric and iterated nonlinear maps, 2 vols., AMS 1988
• Differential-delay equations with two time lags, Memoirs AMS 1978

References

1. biographical information from American Men and Women of Science, Thomson Gale 2004
2. Web site: Roger D. Nussbaum. Mathematics Department, Rutgers University.