Temur, Faruk

Profile URL
https://hdl.handle.net/11147/15929
Name Variants
Temur, F
Temur, F.
Job Title
Email Address
faruktemur@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
Status
Current Staff
Website
https://math.iyte.edu.tr/wp-content/uploads/sites/92/2020/02/faruk_temur_cv.pdf
ORCID ID
0000-0003-1519-4082
Scopus Author ID
55279727000
Turkish CoHE Profile ID
Google Scholar ID
nZAVI9QAAAAJ
WoS Researcher ID
C-6030-2018

Sustainable Development Goals

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Documents

8

Citations

10

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2

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Documents

8

Citations

9

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Scholarly Output

8

Articles

6

Views / Downloads

4361/1419

Supervised MSc Theses

1

Supervised PhD Theses

1

WoS Citation Count

1

Scopus Citation Count

2

Patents

0

Projects

0

WoS Citations per Publication

0.13

Scopus Citations per Publication

0.25

Open Access Source

5

Supervised Theses

2

JournalCount
Journal of Functional Analysis2
Turkish Journal of Mathematics2
Georgian Mathematical Journal1
Journal of Fourier Analysis And Applications1
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Scholarly Output Search Results

Now showing 1 - 8 of 8
  • Doctoral Thesis
    Randomization of certain operators in harmonic analysis
    (01. Izmir Institute of Technology, 2024) Sahillioğulları, Cihan; Temur, Faruk
    Bu tezde, stokastik süreçler aracılığıyla rastsallaştırılmış Hardy-Littlewood majorant problemi çalışılmıştır. Rastsallaştırma için durağan süreçler, rastgele yürüyüşler ve Poisson süreçleri kullanılmış ve bu süreçlerle pertürbe edilmiş deterministik kümeler için Hardy-Littlewood majorant özelliğinin neredeyse kesin olarak geçerli olduğu gösterilmiştir. Poisson süreçleri ile Green-Ruzsa kümesi de dahil olmak üzere çok büyük bir seyrek küme sınıfı pertürbe edilmiştir ve Hardy-Littlewood majorant özelliğinin ihmal edilebilir bir olasılıkla geçerliliğini sürdürdüğü gösterilmiştir. Ayrıca, frekansları daha büyük adım boyutuna sahip bir artimetik ilerleme oluşturan bir üstel toplamın L^2-normu ve L^4-normunun beklenen değerlerinin rastsallaştırmadan nasıl etkilendiği incelenmiştir. Dahası, Poisson süreçleriyle rastsallaştırılmış frekanslara sahip üstel toplamların L^n-normlarının, n ∈ 2N, beklenen değeri kestirilmiş ve bu normlar, ortalama anlamda, bölgeler üzerindeki tam sayı koordinatlı noktalar veya diyofant denklemlerinin çözümleri olarak yorumlanır.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Discrete Fractional Integral Operators With Binary Quadratic Forms as Phase Polynomials
    (Academic Press, 2019) Temur, Faruk; Sert, Ezgi
    We give estimates on discrete fractional integral operators along binary quadratic forms. These operators have been studied for 30 years starting with the investigations of Arkhipov and Oskolkov, but efforts have concentrated on cases where the phase polynomial is translation invariant or quasi-translation invariant. This work presents the first results for operators with neither translation invariant nor quasi-translation invariant phase polynomials. (C) 2019 Elsevier Inc. All rights reserved.
  • Master Thesis
    Discrete Fractional Integral Operators and Their Relations To Number Theory
    (Izmir Institute of Technology, 2018) Sert, Ezgi; Temur, Faruk
    The aim of this thesis is to get estimates on discrete fractional integral operators by using number theory. These operators, starting with the studies of Arkipov and Oskolkov, have been investigated for a long time. Fourier analysis and topics related to it have been used in these studies. However, this study will put forward new results on these operators with the help of arithmetic.
  • Article
    The Frequency Function and Its Connections To the Lebesgue Points and the Hardy-Littlewood Maximal Function
    (TÜBİTAK, 2019) Temur, Faruk
    The aim of this work is to extend the recent work of the author on the discrete frequency function to the more delicate continuous frequency function tau, and further to investigate its relations to the Hardy-Littlewood maximal function M, and to the Lebesgue points. We surmount the intricate issue of measurability of tau f by approaching it with a sequence of carefully constructed auxiliary functions for which measurability is easier to prove. After this, we give analogues of the recent results on the discrete frequency function. We then connect the points of discontinuity of Mf for f simple to the zeros of tau f, and to the non-Lebesgue points of f.
  • Article
    Citation - Scopus: 1
    Level Set Estimates for the Discrete Frequency Function
    (Springer Verlag, 2019) Temur, Faruk
    We introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.
  • Article
    A Quantitative Balian-Low Theorem for Higher Dimensions
    (De Gruyter, 2020) Temur, Faruk
    We extend the quantitative Balian-Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor-Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor-Riesz basis generators, two properties for which dimension reduction is possible. © 2018 Walter de Gruyter GmbH, Berlin/Boston 2018.
  • Article
    Discrete Fractional Integrals, Lattice Points on Short Arcs, and Diophantine Approximation
    (TÜBİTAK - Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, 2022) Temur, Faruk
    Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate quadratic polynomials. We achieve this in part by establishing connections to problems on concentration of lattice points on short arcs of conics, whence we study discrete fractional integrals and lattice point concentration from a unified perspective via tools of sieving and diophantine approximation, and prove theorems that are of interest to researchers in both subjects.
  • Article
    Random Exponential Sums and Lattice Points in Regions
    (Academic Press inc Elsevier Science, 2025) Temur, Faruk; Sahilliogullari, Cihan
    In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and L2n(T), n is an element of N norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.