|
|
|
|
References
|
|
| |
| 1. |
S. Artstein, V. D. Milman, S. Z. Szarek, “Duality metric entropy”, Ann. of Math., 159 (2004), 1313–1328 |
| 2. |
D. Bilyk, M. T. Lacey, A. Vagharshakyan, “On the small ball inequality in all dimensions”, J. Funct. Anal., 254 (2008), 2470–2502 |
| 3. |
B. Carl, “Inequalities of Bernstein–Jackson-type and the degree of compactness of operators in Banach spaces”, Ann. Inst. Fourier, 35 (1985), 79–118 |
| 4. |
B. Carl, I. Kyrezi, A. Pajor, “Metric entropy of convex hulls in Banach spaces”, J. London Math. Soc., 60 (1999), 871–896 |
| 5. |
B. Carl, I. Stephani, Entropy, Compactness and Approximation of Operators, Cambridge Univ. Press., Cambridge, 1990 |
| 6. |
F. Cobos, T. Kühn, “Approximation and entropy numbers in Besov spaces of generalized smoothness”, J. Approx. Theory, 160 (2009), 56–70 |
| 7. |
R. M. Dudley, “The sizes of compact subsets of Hilbert space and continuity of Gaussian processes”, J. Funct. Anal., 1 (1967), 290–330 |
| 8. |
T. Dunker, T. Kühn, M. A. Lifshits, W. Linde, “Metric entropy of integration operators and small ball probabilities for the Brownian sheet”, J. Approx. Theory, 101 (1999), 63–77 |
| 9. |
V. Goodman, “Characteristics of normal samples”, Ann. Probab., 16 (1988), 1281–1290 |
| 10. |
Y. Gordon, H. König, C. Schütt, “Geometric and probabilistic estimates for entropy and approximation numbers of operators”, J. Approx. Theory, 49 (1987), 219–239 |
| 11. |
E. Hashorva, M. Lifshits, O. Seleznjev, “Approximation of a random process with variable smoothness”, Mathematical statistics and limit theorems, Springer, Cham, 2015, 189–208 |
| 12. |
H. König, Eigenvalue Distribution of Compact Operators, Birkhäuser, Basel, 1986 |
| 13. |
T. Kühn, “$\gamma$-Radonifying operators and entropy ideals”, Math. Nachr., 107 (1982), 53–58 |
| 14. |
T. Kühn, “Entropy numbers of general diagonal operators”, Rev. Mat. Complut., 18 (2005), 479–491 |
| 15. |
T. Kühn, H.-G. Leopold, W. Sickel, L. Skrzypczak, “Entropy numbers of embeddings of weighted Besov space. II”, Proc. Edinburgh Math. Soc., 49 (2006), 331–359 |
| 16. |
T. Kühn, W. Linde, “Optimal series representation of fractional Brownian sheets”, Bernoulli, 8 (2002), 669–696 |
| 17. |
J. Kuelbs, W. V. Li, “Metric entropy and the small ball problem for Gaussian measures”, J. Funct. Anal., 116 (1993), 133–157 |
| 18. |
W. V. Li, W. Linde, “Approximation, metric entropy and small ball estimates for Gaussian measures”, Ann. Probab., 27 (1999), 1556–1578 |
| 19. |
W. Linde, A. Pietsch, “Mappings of Gaussian measures of cylindrical sets in Banach spaces”, Teor. Verojatnost. i Primenen., 19:3 (1974), 472–487 |
| 20. |
V. D. Milman, G. Pisier, “Gaussian processes and mixed volumes”, Ann. Probab., 15 (1987), 292–304 |
| 21. |
A. Pajor, N. Tomczak-Jaegermann, “Remarques sur les nombres d'entropie d'un opérateur et de son transposé”, C. R. Acad. Sci. Paris, 301 (1985), 743–746 |
| 22. |
A. Pietsch, Eigenvalues and s-Numbers, Cambridge Univ. Press, Cambridge, 1987 |
| 23. |
G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Cambridge Univ. Press, Cambridge, 1989 |
| 24. |
I. Steinwart, “Entropy of $C(K)$-valued operators”, J. Approx. Theory, 103 (2000), 302–328 |
| 25. |
V. N. Sudakov, “Gaussian measures, Cauchy measures and $\epsilon$-entropy”, Soviet Math. Dokl., 10 (1969), 310–313 |
| 26. |
M. Talagrand, “Regularity of Gaussian processes”, Acta Math., 159 (1987), 99–149 |
| 27. |
M. Talagrand, “The small ball problem for the Brownian sheet”, Ann. Probab., 22 (1994), 1331–1354 |
| 28. |
N. Tomczak-Jaegermann, “Dualité des nombres d'entropie pour des opérateurs á valeurs dans un espace de Hilbert”, C. R. Acad. Sci. Paris, 305 (1987), 299–301 |