Papers and books in NSA and analysis


AMS - American Mathematical Society

JSL - Journal of Symbolic Logic

NSA - Nonstandard analysis

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Albeverio S, Fenstad J and Hoegh-Krohn R (1979) singular perturbations and NSA. Trans AMS 252 pp 275-295

Anderson R and Rashid S (1978) A nonstandard characterisation of weak convergence. Proceedings of the AMS 69 pp 327-332

Anderson R (1982) Star-finite representations of measure spaces. Transactions of the AMS 271 pp 667-687

Anderson R (1986) Almost implies near. Trans. of the AMS 296 pp 229-237

Bellenot S (1976) On nonstandard hulls of convex spaces. Canadian Journal of Mathematics 28 pp 141-147

Bernstein A and Robinson A (1966) Solution of an invariant subspace problem of K.T. Smith and P.R. Halmos. Pacific J. Math 16 pp 421-431

Button R (1976) Monads for regular and normal spaces. Notre Dame J. of formal logic 17 pp 449-456

Button R (1977) When do *continous extensions exist? Notre Dame J. of formal logic 18 pp 406-408

Cartier P (1982) Perturbations singulières des equations differentielles ordinaire et analyse non-standard. Asterisque 92-93 pp 21-44

Cutland N (1983) Nonstandard measure theory and its applications. Bulletin of the London Math. Soc. 15 pp 529-589

Diener F and Diener M (1988) Some asymptotic results in ODEs; in NSA and its applications. Cutland N ed Cam. U. Press.

Diener M (1984) The canard unchained or How fast/slow dynamical systems bifurcate. Mathematical Intelligencer Vol 6, No. 3 pp 38-49

Dyre J (1982) Non-standard characterizations of ideals in C(X). Math. Scand. 50 pp 44-54

Farkas E and Szabo M (1984) On the plausibility of nonstandard proofs in analysis. Dialectica 38 pp 297-310

Gordon E (1997) Nonstandard methods in commutative harmonic analysis. Translations of Mathematical Monographs Volume 164, AMS.

Henson C.W. and Moore Jr L (1972) The nonstandard theory of topological vector spaces. Transactions of the AMS 172 pp 405-435

Henson C.W. and Moore Jr L (1973) Invariance of the nonstandard hulls of locally convex spaces. Duke Math. Journal 40 pp 193-205

Henson C.W. (1974) The isomorphism property in NSA and its use in the theory of Banach spaces JSL 39 pp 717-731

Henson C.W. (1975) When do two Banach spaces have isometrically isomorphic nonstandard hulls? Israel J. of Math. 22 pp 57-67

Henson C.W. (1979) Analytic sets, Baire sets, and the standard part map. Canadian J. of Math. 31 pp 663-672

Henson C.W. (1988) Infinitesimals in functional analysis; in NSA and its applications. Cutland N ed. Camb. Univ. Press.

Henson C.W. (1991) Unbounded Loeb measures. Proceedings of the AMS 74 pp 143-150

Kreisel G (1969) Axiomatisations of NSA that are conservative extensions of formal systems for classical standard analysis; in Applications of model theory to algebra, analysis and prob. (Luxemburg W ed) Holt, Rinehart and Winstion NY 1969 pp 93-106

Kudryk T, Lyantse V and Chuiko G (1993) Nearstandardness on finite set. Matematychni Studii, 2, 25-34.

Kudryk T, Lyantse V and Chuiko G (1994) Nearstandard operators. Mat. St., 3, 29-40.

Kudryk T and Lyantse V (1997) Operator-valued charges on finite sets. Mat. St., 7, #2, 145-156.

Loeb P (1973) A combinatorial analogue of Lyapunov's theorem for infinitesimally generated atomic vector measures. Proceedings of the AMS 39 pp 585-586

Loeb P (1976) Applications of NSA to ideal boundaries in potential theory. Israel J. Math 25 pp 154-187

Loeb P (1979) Weak limits of measures and the standard part map. Proc. AMS 77 pp 128-135

Loeb P (1984) A functional approach to nonstandard measure theory. Contemporary Math. 26 pp 251-261

Loeb P (1985) A nonstandard functional approach to Fubini's theorem. Proc AMS 93 #2 pp 343-346

Loeb P (1988) A lattice formulation of real and vector valued integrals; in NSA and its applications, Cutland N ed. Cambridge U. Press.

Lutz R (1983) L'intrusion de l'analyse nonstandard dans l'é&tude des perturbations singuliè&res. Asté&risque 109-110 pp 101-139

Lutz R and Sari T (1982) Applications of NSA to boundary value problems in singular theory; in Lecture notes in Math. 942 Springer 113-135

Lyantse V (1989) On a perturbation that is infinitely small in the strong operator topology. Ukrainian Math. J., 41, 845-847.

Moore L (1976) Hyperfinite extensions of bounded operators on a seperable Hilbert space. Trans. AMS 218 pp 285-295

Moore S (1982) NSA applied to path integral. Nuovo Cim. B 70 pp 227-290

Murakami H, Nakagiri S and Yeh C (1983) Asymptotic behaviour of solutions of nonlinear differential equations with deviating arguments via NSA. Ann. Pol. Math. 41 pp 203-208

Oikkonen J (1985) Harmonic-Analysis and nonstandard Brownian-motion in the plane. Mathematica Scandinavica 57 #2 pp 346-358

Raskovic M (1985) An application of NSA to functional equations. Publ. Inst. Math. Nouv. Sci. 37 pp 23-24

Robert A (1995) Functional analysis and NSA; in Devel. in nonstandard math. (ed Cutland N and Neves V) Longman.

Stroyan K (1983) Locally convex infinitesimal calculus. Two computations on Mackey (L-infinity). J. of functional analysis 53 #1 pp 1-15

Stroyan K (1988) Superinfinitesimals and inductive limits; in NSA and its applications. Cutland N ed. Cam. U. Press.

Troesch A and Urlacher E (1978) Perturbations singuliè&res et analyse non standard. C.R. Acad. Sc. Paris 287 pp 937-939

Tuckey C (1993) Nonstandard Methods in the Calculus of Variations. Pitman Research Notes in Mathematics 297, Longman House (Addison Wesley Longman) Harlow, Essex. Originally copublished in the United States by John Wiley and Sons, 1993.

Van Den Berg, Imme (1987) Nonstandard asymptotic analysis. Lecture Notes in Math. 1249, Springer-Verlag

Wattenberg F (1977) Nonstandard measure theory - Hausdorff measure. Proc. AMS 65

Zvonkin A and Shubin M (1984) NSA and singular perturbations of ODEs. Russian Math. Surveys 39 #2 pp 69-131