Kushpel, Alexander

Profile URL
https://hdl.handle.net/20.500.12416/8659
Name Variants
Kushpel, A. K. & 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
Status
Current Staff
Website
ORCID ID
0000-0002-9585-744X
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Files
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Scholarly Output

18

Articles

16

Views / Downloads

854/30

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

28

Scopus Citation Count

30

Patents

0

Projects

0

WoS Citations per Publication

1.56

Scopus Citations per Publication

1.67

Open Access Source

9

Supervised Theses

0

JournalCount
Journal of Complexity4
Turkish Journal of Mathematics4
Journal of Mathematical Analysis2
Discrete and Continuous Dynamical Systems - Series S2
Sbornik: Mathematics1
Current Page: 1 / 2

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2019 - 201922020 - 202516

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Scholarly Output Search Results

Now showing 1 - 10 of 18
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Estimates 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
    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.
  • Book
    Optimal Approximation and Pricing of High- Dimensional Options
    (Lambert Academic Publishing, 2019) Kushpel, Alexander
    The 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
    Interpolation of Exponential-Type Functions on a Uniform Grid by Shifts of a Basis Function
    (American Institute of Mathematical Sciences, 2021) Sun, Xinping; Kushpel, Alexander; Levesley, Jeremy; Jarad, Fahd
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On 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.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    The Lebesgue Constants on Projective Spaces
    (Tubitak, 2021) Kushpel, Alexander
    We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].
  • Article
    Citation - Scopus: 1
    A Method of Inversion of Fourier Transforms Ans Its Applications
    (Academic Publications Ltd., 2019) Kushpel, A.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Lower Bounds of Cowidths and Widths of Multiplier Operators
    (Academic Press inc Elsevier Science, 2022) Kushpel, Alexander
    The 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: 3
    Citation - Scopus: 2
    On 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.
  • Book
    Methods of Financial Mathematics
    (LAMBERT Academic Publishing, 2020) Kushpel, Alexander