Hinrichs, Aicke; Prochno, Joscha; Sonnleitner, Mathias Random sections of \(\ell_p\)-ellipsoids, optimal recovery and Gelfand numbers of diagonal operators. (English) Zbl 07720797 J. Approx. Theory 293, Article ID 105919, 19 p. (2023). MSC: 52A22 60D05 52A23 65Y20 60G15 PDFBibTeX XMLCite \textit{A. Hinrichs} et al., J. Approx. Theory 293, Article ID 105919, 19 p. (2023; Zbl 07720797) Full Text: DOI arXiv
Vasil’eva, A. A. Kolmogorov widths of the intersection of two finite-dimensional balls in a mixed norm. (English. Russian original) Zbl 1528.41072 Math. Notes 113, No. 4, 584-586 (2023); translation from Mat. Zametki 113, No. 4, 604-606 (2023). MSC: 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Math. Notes 113, No. 4, 584--586 (2023; Zbl 1528.41072); translation from Mat. Zametki 113, No. 4, 604--606 (2023) Full Text: DOI
Kushpel, Alexander; Taş, Kenan; Levesley, Jeremy Widths and entropy of sets of smooth functions on compact homogeneous manifolds. (English) Zbl 1522.41012 Turk. J. Math. 45, No. 1, 167-184 (2021). Reviewer: Andriy Prymak (Winnipeg) MSC: 41A46 42B15 53C30 PDFBibTeX XMLCite \textit{A. Kushpel} et al., Turk. J. Math. 45, No. 1, 167--184 (2021; Zbl 1522.41012) Full Text: DOI
Hinrichs, Aicke; Prochno, Joscha; Vybíral, Jan Gelfand numbers of embeddings of Schatten classes. (English) Zbl 1480.46018 Math. Ann. 380, No. 3-4, 1563-1593 (2021). Reviewer: Andreas Defant (Oldenburg) MSC: 46B07 47B10 47B06 46B06 46B28 68Q25 PDFBibTeX XMLCite \textit{A. Hinrichs} et al., Math. Ann. 380, No. 3--4, 1563--1593 (2021; Zbl 1480.46018) Full Text: DOI arXiv
Gluskin, Efim D.; Ostrover, Yaron A remark on projections of the rotated cube to complex lines. (English) Zbl 1378.53098 Klartag, Bo’az (ed.) et al., Geometric aspects of functional analysis. Israel seminar (GAFA) 2014–2016. Cham: Springer (ISBN 978-3-319-45281-4/pbk; 978-3-319-45282-1/ebook). Lecture Notes in Mathematics 2169, 137-149 (2017). Reviewer: Viktor Ohanyan (Erevan) MSC: 53D35 52A20 PDFBibTeX XMLCite \textit{E. D. Gluskin} and \textit{Y. Ostrover}, Lect. Notes Math. 2169, 137--149 (2017; Zbl 1378.53098) Full Text: DOI arXiv
Vasil’eva, A. A. Estimates for the widths of discrete function classes generated by a two-weight summation operator. (English. Russian original) Zbl 1366.46014 Proc. Steklov Inst. Math. 294, 291-307 (2016); translation from Tr. Mat. Inst. Steklova 294, 308-324 (2016). MSC: 46B45 41A46 47B36 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Proc. Steklov Inst. Math. 294, 291--307 (2016; Zbl 1366.46014); translation from Tr. Mat. Inst. Steklova 294, 308--324 (2016) Full Text: DOI
Pesenson, Isaac Z. Estimates of Kolmogorov, Gelfand and linear \(n\)-widths on compact Riemannian manifolds. (English) Zbl 1339.43004 Proc. Am. Math. Soc. 144, No. 7, 2985-2998 (2016). Reviewer: Jacques Faraut (Paris) MSC: 43A85 41A17 41A10 53C21 PDFBibTeX XMLCite \textit{I. Z. Pesenson}, Proc. Am. Math. Soc. 144, No. 7, 2985--2998 (2016; Zbl 1339.43004) Full Text: DOI arXiv
Vasil’eva, A. A. Widths of Sobolev weight classes on a domain with cusp. (English. Russian original) Zbl 1350.41026 Sb. Math. 206, No. 10, 1375-1409 (2015); translation from Mat. Sb. 206, No. 10, 37-70 (2015). Reviewer: Naokant Deo (Delhi) MSC: 41A35 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Sb. Math. 206, No. 10, 1375--1409 (2015; Zbl 1350.41026); translation from Mat. Sb. 206, No. 10, 37--70 (2015) Full Text: DOI
Nguyen, Van Kien Bernstein numbers of embeddings of isotropic and dominating mixed Besov spaces. (English) Zbl 1326.41026 Math. Nachr. 288, No. 14-15, 1694-1717 (2015). MSC: 41A25 PDFBibTeX XMLCite \textit{V. K. Nguyen}, Math. Nachr. 288, No. 14--15, 1694--1717 (2015; Zbl 1326.41026) Full Text: DOI arXiv
Vasil’eva, A. A. Widths of weighted Sobolev classes whose weights are functions of the distance to an \(h\)-set. (English. Russian original) Zbl 1329.46036 Dokl. Math. 90, No. 3, 685-687 (2014); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 2, 142-144 (2014). MSC: 46E35 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Dokl. Math. 90, No. 3, 685--687 (2014; Zbl 1329.46036); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 459, No. 2, 142--144 (2014) Full Text: DOI
Romanyuk, A. S. On the problem of linear widths of the classes \(B_{p,\theta}^r\) of periodic functions of many variables. (English. Ukrainian original) Zbl 1309.41014 Ukr. Math. J. 66, No. 7, 1085-1098 (2014); translation from Ukr. Mat. Zh. 66, No. 7, 970-982 (2014). MSC: 41A46 42A10 PDFBibTeX XMLCite \textit{A. S. Romanyuk}, Ukr. Math. J. 66, No. 7, 1085--1098 (2014; Zbl 1309.41014); translation from Ukr. Mat. Zh. 66, No. 7, 970--982 (2014) Full Text: DOI
Derev’yanko, N. V. Estimations of linear widths of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables in the space \(L_q\). (English. Ukrainian original) Zbl 1309.41013 Ukr. Math. J. 66, No. 7, 1013-1027 (2014); translation from Ukr. Mat. Zh. 66, No. 7, 909-921 (2014). MSC: 41A46 42A10 PDFBibTeX XMLCite \textit{N. V. Derev'yanko}, Ukr. Math. J. 66, No. 7, 1013--1027 (2014; Zbl 1309.41013); translation from Ukr. Mat. Zh. 66, No. 7, 909--921 (2014) Full Text: DOI
Koltchinskii, Vladimir; Minsker, Stanislav \(L_1\)-penalization in functional linear regression with subgaussian design. (Pénalisation \(L_1\) en régression fonctionnelle linéaire avec design sous-gaussien.) (English. French summary) Zbl 1308.62143 J. Éc. Polytech., Math. 1, 269-330 (2014). MSC: 62J05 62G05 62J07 PDFBibTeX XMLCite \textit{V. Koltchinskii} and \textit{S. Minsker}, J. Éc. Polytech., Math. 1, 269--330 (2014; Zbl 1308.62143) Full Text: DOI arXiv
Zhang, Shun; Fang, Gensun Widths of embeddings of 2-microlocal Besov spaces. (English) Zbl 1290.41020 J. Approx. Theory 179, 33-62 (2014). Reviewer: Yuri A. Farkov (Moskva) MSC: 41A46 41A65 42B35 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{G. Fang}, J. Approx. Theory 179, 33--62 (2014; Zbl 1290.41020) Full Text: DOI arXiv
Vasil’eva, A. A. Widths of weighted Sobolev classes on a John domain. (English. Russian original) Zbl 1296.46030 Proc. Steklov Inst. Math. 280, 91-119 (2013); translation from Tr. Mat. Inst. Steklova 280, 97-125 (2013). MSC: 46E30 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Proc. Steklov Inst. Math. 280, 91--119 (2013; Zbl 1296.46030); translation from Tr. Mat. Inst. Steklova 280, 97--125 (2013) Full Text: DOI arXiv
Toth, Gabor Notes on Schneider’s stability estimates for convex sets. (English) Zbl 1307.52005 J. Geom. 104, No. 3, 585-598 (2013). Reviewer: Horst Martini (Chemnitz) MSC: 52A40 52A21 54E45 PDFBibTeX XMLCite \textit{G. Toth}, J. Geom. 104, No. 3, 585--598 (2013; Zbl 1307.52005) Full Text: DOI
Vasil’eva, A. A. Kolmogorov widths and approximation numbers of Sobolev classes with singular weights. (English. Russian original) Zbl 1275.41033 St. Petersbg. Math. J. 24, No. 1, 1-27 (2013); translation from Algebra Anal. 24, No. 1, 3-39 (2012). MSC: 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, St. Petersbg. Math. J. 24, No. 1, 1--27 (2013; Zbl 1275.41033); translation from Algebra Anal. 24, No. 1, 3--39 (2012) Full Text: DOI
Zhang, Shun; Fang, Gensun Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces. (English) Zbl 1258.47033 J. Complexity 28, No. 2, 209-223 (2012). Reviewer: Yang Dachun (Beijing) MSC: 47B06 46E35 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{G. Fang}, J. Complexity 28, No. 2, 209--223 (2012; Zbl 1258.47033) Full Text: DOI arXiv
Vasil’eva, A. A. Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights. II. (English) Zbl 1321.46040 Russ. J. Math. Phys. 18, No. 4, 465-504 (2011). MSC: 46E35 41A46 47B06 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Russ. J. Math. Phys. 18, No. 4, 465--504 (2011; Zbl 1321.46040) Full Text: DOI
Vasil’eva, A. A. Kolmogorov widths of weighted Sobolev classes on a domain for a special class of weights. (English) Zbl 1272.46029 Russ. J. Math. Phys. 18, No. 3, 353-385 (2011). Reviewer: Manfred Möller (Johannesburg) MSC: 46E35 41A46 47B06 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Russ. J. Math. Phys. 18, No. 3, 353--385 (2011; Zbl 1272.46029) Full Text: DOI
Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald Compressed sensing and best \(k\)-term approximation. (English) Zbl 1206.94008 J. Am. Math. Soc. 22, No. 1, 211-231 (2009). MSC: 94A12 15B52 94A15 68P30 41A46 PDFBibTeX XMLCite \textit{A. Cohen} et al., J. Am. Math. Soc. 22, No. 1, 211--231 (2009; Zbl 1206.94008) Full Text: DOI
Vasil’eva, A. A. Kolmogorov widths of weighted Sobolev classes on closed intervals. (English. Russian original) Zbl 1219.41017 Math. Notes 84, No. 5, 631-635 (2008); translation from Mat. Zametki 84, No. 5, 676-680 (2008). MSC: 41A46 PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Math. Notes 84, No. 5, 631--635 (2008; Zbl 1219.41017); translation from Mat. Zametki 84, No. 5, 676--680 (2008) Full Text: DOI
Dahlke, Stephan; Novak, Erich; Sickel, Winfried Optimal approximation of elliptic problems by linear and nonlinear mappings. II. (English) Zbl 1102.65061 J. Complexity 22, No. 4, 549-603 (2006). MSC: 65J10 47A50 35J05 65N30 65N15 65Y20 PDFBibTeX XMLCite \textit{S. Dahlke} et al., J. Complexity 22, No. 4, 549--603 (2006; Zbl 1102.65061) Full Text: DOI arXiv
Hinrichs, Aicke; Michels, Carsten Gelfand numbers of identity operators between symmetric sequence spaces. (English) Zbl 1105.47019 Positivity 10, No. 1, 111-133 (2006). Reviewer: Shanli Sun (Beijing) MSC: 47B06 47B37 46B07 46B70 PDFBibTeX XMLCite \textit{A. Hinrichs} and \textit{C. Michels}, Positivity 10, No. 1, 111--133 (2006; Zbl 1105.47019) Full Text: DOI
Gilewicz, J.; Konovalov, V. N.; Leviatan, D. Widths and shape-preserving widths of Sobolev-type classes of \(s\)-monotone functions. (English) Zbl 1096.41019 J. Approximation Theory 140, No. 2, 101-126 (2006). Reviewer: Yuly Makovoz (Lowell) MSC: 41A46 PDFBibTeX XMLCite \textit{J. Gilewicz} et al., J. Approx. Theory 140, No. 2, 101--126 (2006; Zbl 1096.41019) Full Text: DOI
Creutzig, Jakob Approximation of \(S \alpha S\) Lévy processes in \(L_p\) norm. (English) Zbl 1092.41017 J. Approximation Theory 140, No. 1, 71-85 (2006). Reviewer: Yuly Makovoz (Lowell) MSC: 41A46 60G52 PDFBibTeX XMLCite \textit{J. Creutzig}, J. Approx. Theory 140, No. 1, 71--85 (2006; Zbl 1092.41017) Full Text: DOI
Skrzypczak, Leszek On approximation numbers of Sobolev embeddings of weighted function spaces. (English) Zbl 1088.46018 J. Approximation Theory 136, No. 1, 91-107 (2005); corrigendum ibid. 156, No. 1, 116-119 (2009). Reviewer: Dorothee Haroske (Jena) (MR2165121) MSC: 46E35 47B06 PDFBibTeX XMLCite \textit{L. Skrzypczak}, J. Approx. Theory 136, No. 1, 91--107 (2005; Zbl 1088.46018) Full Text: DOI
Brown, Gavin; Dai, Feng Approximation of smooth functions on compact two-point homogeneous spaces. (English) Zbl 1076.41012 J. Funct. Anal. 220, No. 2, 401-423 (2005). Reviewer: Yuly Makovoz (Lowell) MSC: 41A46 41A17 PDFBibTeX XMLCite \textit{G. Brown} and \textit{F. Dai}, J. Funct. Anal. 220, No. 2, 401--423 (2005; Zbl 1076.41012) Full Text: DOI arXiv
Brown, Gavin; Feng, Dai; Sheng, Sun Yong Kolmogorov width of classes of smooth functions on the sphere \(\mathbb S^{d-1}\). (English) Zbl 1036.41012 J. Complexity 18, No. 4, 1001-1023 (2002). Reviewer: Yuly Makovoz (Lowell) MSC: 41A46 PDFBibTeX XMLCite \textit{G. Brown} et al., J. Complexity 18, No. 4, 1001--1023 (2002; Zbl 1036.41012) Full Text: DOI
Konovalov, V. N.; Leviatan, D. Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval. II. (English) Zbl 0992.41013 J. Approximation Theory 113, No. 2, 266-297 (2001). Reviewer: Saulius Norvidas (Vilnius) MSC: 41A46 46A35 PDFBibTeX XMLCite \textit{V. N. Konovalov} and \textit{D. Leviatan}, J. Approx. Theory 113, No. 2, 266--297 (2001; Zbl 0992.41013) Full Text: DOI
Kushpel, Alexander Optimal approximation on \(S^d\). (English) Zbl 0960.41018 J. Complexity 16, No. 2, 424-458 (2000). Reviewer: Li Dengfeng (Nanjing) MSC: 41A46 PDFBibTeX XMLCite \textit{A. Kushpel}, J. Complexity 16, No. 2, 424--458 (2000; Zbl 0960.41018) Full Text: DOI
Edmunds, David E.; Haroske, Dorothee D. Embeddings in spaces of Lipschitz type, entropy and approximation numbers, and applications. (English) Zbl 0997.41022 J. Approximation Theory 104, No. 2, 226-271 (2000). Reviewer: Shi Ying-Guang (Beijing) MSC: 41A65 PDFBibTeX XMLCite \textit{D. E. Edmunds} and \textit{D. D. Haroske}, J. Approx. Theory 104, No. 2, 226--271 (2000; Zbl 0997.41022) Full Text: DOI
Caetano, António M. About approximation numbers in function spaces. (English) Zbl 0915.46026 J. Approximation Theory 94, No. 3, 383-395 (1998). Reviewer: H.Triebel (Jena) MSC: 46E35 47B06 PDFBibTeX XMLCite \textit{A. M. Caetano}, J. Approx. Theory 94, No. 3, 383--395 (1998; Zbl 0915.46026) Full Text: DOI
Babaev, M.-B. A. Approximation to the Sobolev classes \(W_q^r\) of functions of several variables by bilinear forms in \(L_p\) for \(2\leq q\leq p\leq\infty\). (English. Russian original) Zbl 0918.41029 Math. Notes 62, No. 1, 15-29 (1997); translation from Mat. Zametki 62, No. 1, 18-34 (1997). Reviewer: B.Rubin (Jerusalem) MSC: 41A63 PDFBibTeX XMLCite \textit{M. B. A. Babaev}, Math. Notes 62, No. 1, 15--29 (1997; Zbl 0918.41029); translation from Mat. Zametki 62, No. 1, 18--34 (1997) Full Text: DOI
Galeev, È. M. Linear widths of Hölder-Nikol’skij classes of periodic functions of several variables. (English. Russian original) Zbl 0886.46036 Math. Notes 59, No. 2, 133-140 (1996); translation from Mat. Zametki 59, No. 2, 189-199 (1996). MSC: 46E35 PDFBibTeX XMLCite \textit{È. M. Galeev}, Math. Notes 59, No. 2, 133--140 (1996; Zbl 0886.46036); translation from Mat. Zametki 59, No. 2, 189--199 (1996) Full Text: DOI
Vakarchuk, S. B. On the diameters of some classes of analytic functions. I. (English. Russian original) Zbl 0788.30040 Ukr. Math. J. 44, No. 3, 283-291 (1992); translation from Ukr. Mat. Zh. 44, No. 3, 324-333 (1992). MSC: 30H05 30E10 30D55 PDFBibTeX XMLCite \textit{S. B. Vakarchuk}, Ukr. Math. J. 44, No. 3, 283--291 (1992; Zbl 0788.30040); translation from Ukr. Mat. Zh. 44, No. 3, 324--333 (1992) Full Text: DOI
Dinh-Dung The sampling theorem, \(L^ T_ q\)-approximation and \(\epsilon\)- dimension. (English) Zbl 0766.41035 J. Approximation Theory 70, No. 1, 1-15 (1992). Reviewer: S.Cobzaş (Cluj-Napoca) MSC: 41A65 41A46 94A11 PDFBibTeX XMLCite \textit{Dinh-Dung}, J. Approx. Theory 70, No. 1, 1--15 (1992; Zbl 0766.41035) Full Text: DOI
Gluskin, E. D.; Tomczak-Jaegermann, N.; Tzafriri, L. Subspaces of \(\ell^ N_ p\) of small codimension. (English) Zbl 0792.46010 Isr. J. Math. 79, No. 2-3, 173-192 (1992). Reviewer: E.Behrends (Berlin) MSC: 46B25 46B07 PDFBibTeX XMLCite \textit{E. D. Gluskin} et al., Isr. J. Math. 79, No. 2--3, 173--192 (1992; Zbl 0792.46010) Full Text: DOI
Mathé, Peter Random approximation of Sobolev embeddings. (English) Zbl 0735.65004 J. Complexity 7, No. 3, 261-281 (1991). Reviewer: K.G.Brokate MSC: 65D15 65Y20 65C05 46E35 41A99 PDFBibTeX XMLCite \textit{P. Mathé}, J. Complexity 7, No. 3, 261--281 (1991; Zbl 0735.65004) Full Text: DOI
Gordon, Y.; König, H.; Schütt, C. Geometric and probabilistic estimates for entropy and approximation numbers of operators. (English) Zbl 0647.47035 J. Approximation Theory 49, 219-239 (1987). Reviewer: A.L.Brown MSC: 47B10 46B20 41A45 41A46 PDFBibTeX XMLCite \textit{Y. Gordon} et al., J. Approx. Theory 49, 219--239 (1987; Zbl 0647.47035) Full Text: DOI
Pajor, Alain; Tomczak-Jaegermann, Nicole Subspaces of small codimension of finite-dimensional Banach spaces. (English) Zbl 0623.46008 Proc. Am. Math. Soc. 97, 637-642 (1986). Reviewer: P.L.Papini MSC: 46B20 47B10 46B03 47B06 PDFBibTeX XMLCite \textit{A. Pajor} and \textit{N. Tomczak-Jaegermann}, Proc. Am. Math. Soc. 97, 637--642 (1986; Zbl 0623.46008) Full Text: DOI
Gluskin, E. D. The octahedron is badly approximated by random subspaces. (English. Russian original) Zbl 0619.46014 Funct. Anal. Appl. 20, 11-16 (1986); translation from Funkts. Anal. Prilozh. 20. No. 1, 14-20 (1986). Reviewer: J. Daneš MSC: 46B20 46B25 PDFBibTeX XMLCite \textit{E. D. Gluskin}, Funct. Anal. Appl. 20, 11--16 (1986; Zbl 0619.46014); translation from Funkts. Anal. Prilozh. 20. No. 1, 14--20 (1986) Full Text: DOI
Carl, Bernd Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces. (English) Zbl 0564.47009 Ann. Inst. Fourier 35, No. 3, 79-118 (1985). MSC: 47B10 47L30 47B38 PDFBibTeX XMLCite \textit{B. Carl}, Ann. Inst. Fourier 35, No. 3, 79--118 (1985; Zbl 0564.47009) Full Text: DOI Numdam EuDML