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Persson, Lars-Erik
Publications (10 of 364) Show all publications
Kopezhanova, A., Nursultanov, E. & Persson, L.-E. (2018). A new generalization of boas theorem for some lorents spaces lambda(q)(omega). Journal of Mathematical Inequalities, 12(3), 619-633
Open this publication in new window or tab >>A new generalization of boas theorem for some lorents spaces lambda(q)(omega)
2018 (English)In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 619-633Article in journal (Refereed) Published
Abstract [en]

Let Lambda(q)(omega), q > 0, denote the Lorentz space equipped with the (quasi) norm parallel to f parallel to(Lambda q(omega)) := (integral(1)(0) (f*(t)omega(t))(q)dt/t)(1/q) for a function integral on [0,1] and with omega positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system Phi = {phi(k)}(k=1)(infinity) and generalized Lorentz Lambda(q) (omega) spaces.

Place, publisher, year, edition, pages
Element, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-71213 (URN)10.7153/jmi-2018-12-47 (DOI)000445366500002 ()
Note

Validerad;2018,Nivå 2;2018-10-15 (johcin)

Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2018-10-15Bibliographically approved
Blahota, I., Nagy, K., Persson, L.-E. & Tephnadze, G. (2018). A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces. Georgian Mathematical Journal
Open this publication in new window or tab >>A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces
2018 (Estonian)In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176Article in journal (Refereed) Epub ahead of print
Abstract [en]

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H-{p}} to the Lebesgue space L p {L-{p}} for all 0 < p ≤ 1 {0<p\leq 1}. We also prove that the result is sharp in a particular sense. 

Place, publisher, year, edition, pages
Walter de Gruyter, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-71225 (URN)10.1515/gmj-2018-0045 (DOI)
Available from: 2018-10-16 Created: 2018-10-16 Last updated: 2018-10-16
Niculescu, C. P. & Persson, L.-E. (2018). Convex Functions and Their Applications: A Contemporary Approach. Cham: Springer
Open this publication in new window or tab >>Convex Functions and Their Applications: A Contemporary Approach
2018 (English)Book (Refereed)
Abstract [en]

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics.  The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples.  Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.

This book can serve as a reference and source of inspiration to researchers in several branches of mathematics and engineering, and it can also be used as a reference text for graduate courses on convex functions and applications.

Place, publisher, year, edition, pages
Cham: Springer, 2018. p. 415
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69635 (URN)10.1007/978-3-319-78337-6 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convex Functions on a Normed Linear Space. In: Duality and Convex Optimization: (pp. 107-184). Cham: Springer
Open this publication in new window or tab >>Convex Functions on a Normed Linear Space
2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 107-184Chapter in book (Refereed)
Abstract [en]

Convex functions and their relatives are ubiquitous in a large variety of applications such as optimization theory, mass transportation, mathematical economics, and geometric inequalities related to isoperimetric problems. This chapter is devoted to a succinct presentation of their theory in the context of real normed linear spaces, but most of the illustrations will refer to the Euclidean space RN,">RN,RN, the matrix space MN(R)">MN(R)MN(R) of all N&#x00D7;N">N×NN×N-dimensional real matrices (endowed with the Hilbert–Schmidt norm or with the operator norm), and the Lebesgue spaces Lp(RN)">Lp(RN)Lp(RN) with p&#x2208;[1,&#x221E;]">p∈[1,∞]p∈[1,∞].

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69632 (URN)10.1007/978-3-319-78337-6_3 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convex Functions on Intervals. In: Duality and Convex Optimization: (pp. 1-70). Cham: Springer
Open this publication in new window or tab >>Convex Functions on Intervals
2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 1-70Chapter in book (Refereed)
Abstract [en]

 The study of convex functions of one real variable offers an excellent glimpse of the beauty and fascination of advanced mathematics. The reader will find here a large variety of results based on simple and intuitive arguments that have remarkable applications. At the same time they provide the starting point of deep generalizations in the setting of several variables, that will be discussed in the next chapters.

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69631 (URN)10.1007/978-3-319-78337-6_1 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convex Sets in Real Linear Spaces. In: Convex Functions and Their Applications: A Contemporary Approach (pp. 71-106). Cham: Springer
Open this publication in new window or tab >>Convex Sets in Real Linear Spaces
2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 71-106Chapter in book (Refereed)
Abstract [en]

The natural domain for a convex function is a convex set. In this chapter we review some basic facts, necessary for a deep understanding of the concept of convexity in real linear spaces. For reader’s convenience, all results concerning the separation of convex sets in Banach spaces are stated in Section 2.2 with proofs covering only the particular (but important) case of Euclidean spaces. Full details in the general case are to be found in Appendix  B

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69578 (URN)10.1007/978-3-319-78337-6_2 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convexity and Majorization. In: Convex Functions and Their Applications: A Contemporary Approach (pp. 185-226). Cham: Springer
Open this publication in new window or tab >>Convexity and Majorization
2018 (English)In: Convex Functions and Their Applications: A Contemporary Approach, Cham: Springer, 2018, p. 185-226Chapter in book (Refereed)
Abstract [en]

This chapter is aimed to offer a glimpse on the majorization theory and the beautiful inequalities associated to it. Introduced by G. H. Hardy, J. E. Littlewood, and G. Pólya (Messenger Math. 58:145–152, (1929), [208]) in 1929, and popularized by their celebrated book on Inequalities (Hardy et al., Inequalities, Cambridge University Press, 1952, [209]), the relation of majorization has attracted along the time a big deal of attention not only from the mathematicians, but also from people working in various other fields such as statistics, economics, physics, signal processing, data mining, etc. Part of this research activity is summarized in the 900 pages of the recent book by A. W. Marshall, I. Olkin, and B. Arnold (Inequalities: theory of majorization and its applications. Springer, New York (2011), [305]).

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69580 (URN)10.1007/978-3-319-78337-6_4 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convexity and Majorization. In: Duality and Convex Optimization: (pp. 255-300). Cham: Springer
Open this publication in new window or tab >>Convexity and Majorization
2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 255-300Chapter in book (Refereed)
Abstract [en]

 Convex optimization is one of the main applications of the theory of convexity and Legendre–Fenchel duality is a basic tool, making more flexible the approach of many concrete problems. The diet problem, the transportation problem, and the optimal assignment problem are among the many problems that during the Second World War and immediately after led L. Kantorovich, T. C. Koopmans, F. L. Hitchcock, and G. B. Danzig to develop the mathematical theory of linear programming. Soon it was realized that most results extend to the framework of convex functions, which marked the birth of convex programming. Later on, W. Fenchel, R. T. Rockafellar, and J. J. Moreau laid the foundations of convex analysis.

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69630 (URN)10.1007/978-3-319-78337-6_6 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved
Niculescu, C. P. & Persson, L.-E. (2018). Convexity in Spaces of Matrices. In: Duality and Convex Optimization: (pp. 227-254). Cham: Springer
Open this publication in new window or tab >>Convexity in Spaces of Matrices
2018 (English)In: Duality and Convex Optimization, Cham: Springer, 2018, p. 227-254Chapter in book (Refereed)
Abstract [en]

In this chapter we investigate three subjects concerning the convexity of functions defined on a space of matrices (or just on a convex subset of it). The first one is devoted to the convex spectral functions, that is, to the convex functions F:Sym(n,R)&#x2192;R">F:Sym(n,R)→RF:Sym(n,R)→R whose values F(A) depend only on the spectrum of A. The main result concerns their description as superpositions f&#x2218;&#x039B;">f∘Λf∘Λ between convex functions f:Rn&#x2192;R">f:Rn→Rf:Rn→R invariant under permutations, and the eigenvalues map &#x039B;">ΛΛ.

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
CMS Books in Mathematics, ISSN 1613-5237
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-69633 (URN)10.1007/978-3-319-78337-6_5 (DOI)978-3-319-78336-9 (ISBN)978-3-319-78337-6 (ISBN)
Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-18Bibliographically approved
Abramovich, S. & Persson, L.-E. (2018). Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities. Mathematical Inequalities & Applications, 21(3), 759-772
Open this publication in new window or tab >>Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities
2018 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 3, p. 759-772Article in journal (Refereed) Published
Abstract [en]

In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

Place, publisher, year, edition, pages
Element, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-70848 (URN)10.7153/mia-2018-21-54 (DOI)000444628200011 ()2-s2.0-85052715296 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-09-12 (svasva)

Available from: 2018-09-12 Created: 2018-09-12 Last updated: 2018-10-10Bibliographically approved
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