Kushpel, Alexander
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Name Variants
Kushpel, A. K.
Kushpel, A.
Kushpel, A.
Job Title
Dr. Öğr. Üyesi
Email Address
kushpel@cankaya.edu.tr
Main Affiliation
02.02. Matematik
Matematik
02. Fen-Edebiyat Fakültesi
01. Çankaya Üniversitesi
Matematik
02. Fen-Edebiyat Fakültesi
01. Çankaya Üniversitesi
Status
Current Staff
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Scopus Author ID
Turkish CoHE Profile ID
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WoS Researcher ID
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Scholarly Output
14
Articles
12
Views / Downloads
844/23
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
28
Scopus Citation Count
29
WoS h-index
3
Scopus h-index
3
Patents
0
Projects
0
WoS Citations per Publication
2.00
Scopus Citations per Publication
2.07
Open Access Source
5
Supervised Theses
0
Google Analytics Visitor Traffic
| Journal | Count |
|---|---|
| Journal of Complexity | 4 |
| Turkish Journal of Mathematics | 2 |
| Journal of Mathematical Analysis | 1 |
| lnternational Journal of Differential Equations and Applications | 1 |
| Optimal Approximation and Pricing of High- Dimensional Options | 1 |
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14 results
Scholarly Output Search Results
Now showing 1 - 10 of 14
Article John-Lowner Ellipsoids and Entropy of Multiplier Operators on Rank 1 Compact Homogeneous Manifolds(Steklov Mathematical inst, Russian Acad Sciences, 2025) Kushpel, A. K.We present a new method of the evaluation of entropy, which is based on volume estimates for John-Lowner ellipsoids induced by the eigenfunctions of Laplace-Beltrami operator on compact homogeneous manifolds M-d of rank 1. This approach gives the sharp orders of entropy in the situations where the known methods meet difficulties of fundamental nature. In particular, we calculate the sharp orders of the entropy of the Sobolev classes W-p(gamma) (M-d), gamma> 0, in L-q(M-d), 1 <= q <= p <= infinity. Bibliography: 35 titles.Article Citation - WoS: 4Citation - Scopus: 4On the Optimality of the Trigonometric System(Academic Press inc Elsevier Science, 2020) Jarad, Fahd; Kushpel, A.; Tas, K.We study a new phenomenon of the behaviour of widths with respect to the optimality of trigonometric system. It is shown that the trigonometric system is optimal in the sense of Kolmogorov widths in the case of "super-high" and "super-small" smoothness but is not optimal in the intermediate cases. Bernstein's widths behave differently when compared with Kolmogorov in the case of "super-small" smoothness. However, in the case of "super-high" smoothness Kolmogorov and Bernstein widths behave similarly, i.e. are realized by trigonometric polynomials. (C) 2019 Elsevier Inc. All rights reserved.Book Optimal Approximation and Pricing of High- Dimensional Options(Lambert Academic Publishing, 2019) Kushpel, AlexanderThe book introduces an original general approach to the problem of multidimensional pricing which is applicable for a wide range of practically important examples. It gives a comprehensive and self-contained treatment of the problem of multidimensional pricing which provides the reader with all technical details. The book reflects a new stage of research in Quantitative Finance. It gives a particular fascination when apparently disjoint areas turn out to have a meaningful connection to each other. It demonstrates on concrete examples deep connections between Quantitative Finance and Numerical Analysis, Topology, Functional Analysis and Complexity Theory. The book can be considered as an inspirational source for practitioners, graduate and postgraduate students, MSc and PhD projects, to those working in Quantitative Finance and Economics.Article Citation - WoS: 1Citation - Scopus: 1Optimal Recovery and Volume Estimates(Academic Press inc Elsevier Science, 2023) Kushpel, AlexanderWe study volumes of sections of convex origin-symmetric bodies in Rn induced by orthonormal systems on probability spaces. The approach is based on volume estimates of John-Lowner ellipsoids and expectations of norms induced by the respective systems. The estimates obtained allow us to establish lower bounds for the radii of sections which gives lower bounds for Gelfand widths (or linear cowidths). As an application we offer a new method of evaluation of Gelfand and Kolmogorov widths of multiplier operators. In particular, we establish sharp orders of widths of standard Sobolev classes Wp & gamma;, & gamma; > 0 in Lq on two-point homogeneous spaces in the difficult case, i.e. if 1 < q < p < oo.& COPY; 2023 Elsevier Inc. All rights reserved.Book Methods of Financial Mathematics(LAMBERT Academic Publishing, 2020) Kushpel, AlexanderArticle Citation - WoS: 3Citation - Scopus: 3Estimates of Entropy for Multiplier Operators of Systems of Orthonormal Functions(Academic Press inc Elsevier Science, 2023) Milare, J.; Kushpel, A. K.; Tozoni, S. A.We obtain upper and lower estimates for epsilon-entropy and entropy numbers of multiplier operators of systems of orthonormal functions bounded from Lp to Lq. Upper estimates in our study require that a Marcinkiewicz-type multiplier theorem is available for the system. As application we obtain estimates for epsilon-entropy and entropy numbers of the multiplier operators associated with the sequences (k-gamma (lnk)-xi)infinity k=2 and (e-gamma kr )infinity k=0 where gamma > 0, xi >= 0 and 0 < r < 1. Some of these estimates are order sharp. We verify that the trigonometric system on the circle, the Vilenkin system and the Walsh system satisfy the conditions of our study. We also study analogous results for the Haar system and the Walsh systems on spheres.(c) 2022 Elsevier Inc. All rights reserved.Article Citation - Scopus: 1On the Problem of Schoenberg On Rn(Univ Prishtines, 2024) Kushpel, Alexander; Tas, KenanIn 1946 Schoenberg introduced splines on R, which play now one of the central roles in Numerical Analysis, and posed the problem on spline interpolation. The main aim of this article is to establish explicit representations of fundamental splines on Rn and give a positive solution of the problem of Schoenberg on RnArticle Citation - WoS: 6Citation - Scopus: 6The Radii of Sections of Origin-Symmetric Convex Bodies and Their Applications(Academic Press inc Elsevier Science, 2021) Tas, Kenan; Kushpel, AlexanderLet V and W be any convex and origin-symmetric bodies in R-n . Assume that for some A is an element of L (R-n -> R-n), det A not equal 0, V is contained in the ellipsoid A(-1)B((2))(n), where B-(2)(n) is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A(-1) V in terms of the spectral radius of AA and the expectations of parallel to . parallel to(V) and parallel to . parallel to(W)0 with respect to Haar measure on Sn-1 subset of R-n. It is shown that the respective expectations are bounded as n -> infinity in many important cases. As an application we offer a new method of evaluation of n-widths of multiplier operators. As an example we establish sharp orders of n-widths of multiplier operators Lambda : L-p (M-d) -> L-q (M-d), 1 < q <= 2 <= p < infinity on compact homogeneous Riemannian manifolds M-d. Also, we apply these results to prove the existence of flat polynomials on M-d. (c) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Lower Bounds of Cowidths and Widths of Multiplier Operators(Academic Press inc Elsevier Science, 2022) Kushpel, AlexanderThe main objective of this article is to present new results on optimal reconstruction of function classes on probability spaces (Omega, A, nu) in the standard L-q spaces. We consider the problem of optimal reconstruction in the sense of the respective cowidths of standard function classes Lambda U-p generated by multiplier or pseudo differential operators Lambda : L-p -> L-q, 1 <= p, q <= infinity. Our approach is based on the estimates of volumes of John-Lowner ellipsoids and expectations of norms induced by orthonormal systems on (Omega, A, nu). It is shown that the results obtained are order sharp in many cases. In particular, we obtain sharp orders of entropy of Sobolev classes W-infinity(gamma), gamma > 0 in L-1 and n-widths of Lambda U-p in L-q, 1 < q <= p < infinity in the case of two-point homogeneous spaces and torus. (C) 2021 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 2On the Lebesgue Constants(Springer, 2020) Kushpel, A. K.We present the solution of a classical problem of approximation theory about the sharp asymptotics of Lebesgue constants or the norms of Fourier-Laplace projections on the real sphere S-d, in complex P-d (C) and quaternionic P-d(H) projective spaces, and in the Cayley elliptic plane P-16(Cay). In particular, these results supplement the sharp asymptotics established by Fejer (1910) in the case of S-1 and by Gronwall (1914) in the case of S-2.
