The heritage of P. Lévy in geometrical functional analysis

Milman, V. D.

Colloque Paul Lévy sur les processus stochastiques (22-26 juin 1987. École Polytechnique, Palaiseau), Astérisque, no. 157-158 (1988), pp. 273-301.

[Al] N. Alon, Eigenvalues and expanders, Combinatorica 6 (1986), 83-96. | DOI | Zbl

[AlM1] N. Alon, and V. D. Milman, ${\lambda }_1$, isoperimetric inequalities for graphs and superconcentrators, J. Comb. Theory, Ser. B 38 (1985),73-88. | DOI | Zbl

[AmM1] D. Amir and V. D. Milman, Unconditional symmetric sets in $n$-dimensional normed spaces, Isreal J. Math. 37 (1980), 3-20. | DOI | Zbl

[AmM2] D. Amir and V. D. Milman, A quantitative finite-dimensional Krivine theorem, Israel J. Math. 50 (1985), 1-12. | DOI | Zbl

[BLM] J. Bourgain, J. Lindenstrauss and V. Milman, Approximation of zonoids by zonotopes, Preprint I.H.E.S., September 1987, 62pp. | Zbl

[Bo] C. Borell, The Brunn-Minsowski inequality in Gauss spaces, Inventiones Math. 30 (1975), 207-216. | DOI | EuDML | Zbl

[Bor] E. Borel, Introduction géométrique á quelques Théories physiques, Gauthier-Villars, Paris, 1914. | JFM

[CE] J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North Holland, 1975. | Zbl

[Dv] A. Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Symp. on Linear Spaces, Jerusalem 1961, 123-160. | Zbl

[F] M. N. Feller, Infinite dimensional elliptic equations and operators of P. Lévy type. Uspekhi Mat. Nauk, 41 No. 4 (1986), 97-140 (Russian). | Zbl

[FF] P. Frankel and Z. Füredi, A short proof for a theorem of Harper about Hamming spheres, Discrete Math. 34 (1981), 311-313. | DOI | Zbl

[FLM] T. Figiel, J. Lindenstrauss and V. D. Milman, The dimensions of almost spherical sections of convex bodies, Acta Math. 139 (1977), 53-94. | DOI | Zbl

[G] L. Š. Grinblat, Compactifications of spaces of functions and integration of functionals, Trans. AMS, v. 217 (1976), 195-223. | DOI | Zbl

[Gor] Y. Gordon, On Milman's inequality and random subspaces which escape through a mesh in ${ℝ}^n$, Gafa-Seminar 86-87, Lecture Notes in Mathematics, Springer-Verlag. | Zbl

[Gr1] M. Gromov, Paul Levy isoperimetric inequality, Preprint I.H.E.S. 1980.

[Gr2] M. Gromov, Isoperimetric inequalities in Riemannian manifolds, App. I in "Asymptotic Theory of Finite Dimensional Normed Spaces" by V. Milman, G. Schechtman, Springer Lecture Notes 1200 (pp. 114-129). | Zbl

[Gr3] M. Gromov, Filling Riemannian manifolds, J. Diff. Geom 18 (1983), 1-147. | DOI | Zbl

[GrM1] M. Gromov and V. D. Milman, A topological application of the isoperimetric inequality. Amer. J. Math. 105 (1983), 843-854. | DOI | Zbl

[GrM2] M. Gromov and V. D. Milman, Brunn theorem and a concentration of volume of convex bodies, GAFA Seminar Notes, Israel 1983-1984.

[GrM3] M. Gromov, V. D. Milman Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces, Compositio Math. 62, No. 3 (1987), 263-282. | EuDML | Numdam | Zbl

[H] L. H. Harper, Optimal numberings and isoperimetric problems on graphs, J. Comb. Theory 1 (1966), 385-393. | DOI | Zbl

[Hi] T. Hida, Analysis of Brownian functionals, Lecture Notes, IMA, University of Minnesota, 1986.

[K1] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1969), 63-65. | DOI | Zbl

[K2] D. Kazhdan, Private communication.

[L] P. Lévy, Problèmes Concrets d'Analyse Fonctionnelle, Gauthier-Villars, Paris 1951. | Zbl

[Ma] B. Maurey, Constructions de suites symétriques, C.R. Acad. Sci. Paris, Ser A-B 288 (1979), 679-681. | Zbl

[MaP] M. B. Marcus and G. Pisier, Random Fourier series with applications to harmonic analysiss, Ann. Math. Studies, v. 101, Princeton 1981. | Zbl

[M1] V. D. Milman, A new proof of the theorem of A. Dvoretzky on sections of convex bodies, Funkcional. Anal i Proložen. 5 (1971), 28-37 (Russian). | Zbl

[M2] V. D. Milman, Asymptotic properties of functions of several variables defined on homogeneous spaces, DAN SSSR, 199 (1971) No. 6; English transl. Soviet Math. Dokl. 12 (1971) No. 4, 1277-1491. | Zbl

[M3] V. D. Milman, On a property of functions defined on infinite-dimensional manifolds, DAN SSSR, 200 (1971) No. 4, Soviet Math. Dokl. 12 (1971) (translated from Russian), 1487-1491. | Zbl

[M4] V. D. Milman, Geometric theory of Banach spaces II. Geometry of the unit sphere, Russian Math. Survey 26, No. 6, (1971) 80-159 (Translated from Russian). | Zbl

[M5] V. D. Milman, The basis structure of a $B$-space and properties of the sphere which are invariant relative to isomorphisms, Soviet Math. Dokl 9 (1968), 451-454 (translated from Russian). | Zbl

[M6] V. D. Milman, The spectrum of bounded continuous functions which are given on the unit sphere of a $B$-space, Functional Anal. Prilozen 3, No. 2 (1969), 67-79. | Zbl

[M7] V. D. Milman, The infinite dimensional geometry of the unit sphere of a Banach space. Soviet Math. Dokl. 8 (1967), 1440-1444 (translated from Russian). | Zbl

[M8] V. D. Milman Diameter of minimal invariant subsets of Lipshitz actions on compact subsets of $R^k$, GAFA Seminar Notes, Springer-Verlag, Lecture Notes in Matheamtics 1267 (1987) 13-20. | Zbl

[MSch] V. D. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces, Springer Lecture Notes #1200 (1986).

[P] G. Pisier, Probabilistic methods in the geometry of Banach spaces, Probability and Anaysis, Springer-Verlag, Lecture Notes in Math. 1206, 167-241. | Zbl

[Poi] H. Poincaré, Calcul des probabilities, Gauthier-Villars 1912.

[Sch1] G. Schechtman, Lévy type inequality for a class of metric spaces, Martingale theory in harmonic analysis and Banach spaces, Springer-Verlag 1981, 211-215. | Zbl

[Sch2] G. Schechtman, Random embedding of euclidean spaces in sequence spaces, Israel J. Math., 40 (1981) 187-192. | DOI | Zbl

[Sch3] G. Schechtman, More on embedding subspaces of $L_p$ in $l_r^n$, Compositio Math. 61 (1987), 159-170. | EuDML | Numdam | Zbl

[St] W. F. Stout, Almost Sure Convergence, Academic Press, 1974. | Zbl

[WW] D. L. Wang and P. Wang, Extremal configurations on a discrete torus and a generalization of the generalized Macaulay theorem, Siam J. Appl. Math. 33 (1977), 55-59. | DOI | Zbl