| 1. |
- Aleman, Alexandru, et al.
(författare)
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An Hp scale for complete Pick spaces
- 2021
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Ingår i: Studia Mathematica. - 0039-3223. ; 258:3, s. 343-359
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Tidskriftsartikel (refereegranskat)abstract
- We define by interpolation a scale analogous to the Hardy Hp scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call Hp. In particular, we obtain an Hp-Hq duality and establish sharp pointwise estimates for functions in Hp
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| 2. |
- Bakas, Odysseas
(författare)
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Sharp asymptotic estimates for a class of Littlewood-Paley operators
- 2021
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 260:2, s. 195-216
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Tidskriftsartikel (refereegranskat)abstract
- It is well-known that Littlewood-Paley operators formed with respect to lacunary sets of finite order are bounded on Lp(ℝ) for all 1 < p < ∞. In this note it is shown that 'Equation Presented' where SIE2 denotes the classical Littlewood-Paley operator formed with respect to the second order lacunary set E2 = {±(2k -2l) : k, l ∈ ℤ with k > l}. Variants in the periodic setting and for certain lacunary sets of order N are also presented.
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| 3. |
- Kiwerski, Tomasz, et al.
(författare)
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Isomorphic and isometric structure of the optimal domains for Hardy-type operators
- 2021
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Ingår i: Studia Mathematica. - Warszawa : Polskiej Akademii Nauk. - 0039-3223 .- 1730-6337. ; 260:1, s. 45-89
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the structure of optimal domains for the Hardy-type operators including, for example, the classical Cesàro, Copson and Volterra operators as well as some of their generalizations. We prove that, in some sense, the abstract Cesàro and Copson function spaces are closely related to the space L1, namely, they contain “in the middle” a complemented copy of L1[0,1] and an asymptotically isometric copy of ℓ1, and can also be renormed to contain an isometric copy of L1[0,1]. Moreover, generalized Tandori function spaces are quite similar to L∞ because they contain an isometric copy of ℓ∞ and can be renormed to contain an isometric copy of L∞[0,1]. Several applications to the metric fixed point theory will be given. Next, we prove that the Cesàro construction X↦CX does not commute with the truncation operation of the measure space support. We also study whether a given property transfers between a Banach function space X and the space TX, where T is the Cesàro or the Copson operator. In particular, we find a large class of properties which do not lift from TX into X and we prove that abstract Cesàro and Copson function spaces are never reflexive, are not isomorphic to a dual space and do not have the Radon–Nikodym property in general.
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| 4. |
- Kurasov, Pavel, et al.
(författare)
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Gluing graphs and the spectral gap : a Titchmarsh-Weyl matrix-valued function approach
- 2020
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 255:3, s. 303-326
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Tidskriftsartikel (refereegranskat)abstract
- Assume that two metric graphs are joined by gluing a few vertices. We investigate the behaviour of the spectral gap for the corresponding standard Laplacians. It appears that a precise answer can be given in terms of the corresponding Titchmarsh-Weyl (matrix) functions of the two subgraphs, more precisely in terms of their negative spectral subspaces. We illustrate our results by considering explicit examples.
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| 5. |
- McKee, Andrew, 1989
(författare)
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Weak amenability for dynamical systems
- 2021
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Ingår i: Studia Mathematica. - 1730-6337 .- 0039-3223. ; 258:1, s. 53-70
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Tidskriftsartikel (refereegranskat)abstract
- Using the recently developed notion of a Herz-Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a discrete group. We also consider a generalisation of the Fourier algebra and its multipliers to crossed products.
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| 6. |
- McKee, Andrew
(författare)
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Weak amenability for dynamical systems
- 2021
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 258:1, s. 53-70
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Tidskriftsartikel (refereegranskat)abstract
- Using the recently developed notion of a Herz-Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a discrete group. We also consider a generalisation of the Fourier algebra and its multipliers to crossed products.
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| 7. |
- Ohrysko, Przemyslaw, 1988, et al.
(författare)
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Spectrally reasonable measures II
- 2023
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 1730-6337 .- 0039-3223. ; 270:3, s. 285-300
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Tidskriftsartikel (refereegranskat)abstract
- A measure on a locally compact Abelian group is said to have a natural spectrum if its spectrum is equal to the closure of the range of the Fourier-Stieltjes transform. In this paper we continue the study of spectrally reasonable measures (measures perturbing any measure with a natural spectrum to a measure with a natural spectrum) initiated in [P. Ohrysko and M. Wojciechowski, St. Petersburg Math. J. 28 (2017)]. In particular, we provide a full characterization of such measures for a certain class of locally compact Abelian groups which includes the circle and the real line. We also elaborate on the spectral properties of measures with non-natural but real spectra, constructed by F. Parreau.
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| 8. |
- Paulos, Joao Pedro, 1991
(författare)
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Descriptive set-theoretic aspects of closed sets of uniqueness in the non-abelian setting
- 2022
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 1730-6337 .- 0039-3223. ; 265, s. 77-109
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Tidskriftsartikel (refereegranskat)abstract
- We study the family of closed sets of (extended) uniqueness of a locally compact group G which is not necessarily abelian. We prove some preservation properties concerning this family of sets as well as their operator-theoretic counterpart, locate their descriptive complexity and establish sufficient conditions for the non-existence of a Borel basis. 1. Introduction. The study of sets of uniqueness has a long and illus-trious history witnessing fruitful interdisciplinary efforts and the develop-ment of techniques whose range of applicability goes beyond the realm of harmonic analysis. Unequivocally a rich topic, it constitutes a rather fertile soil for unexpected counter-examples and remarkable theorems. Classically, sets of uniqueness (and sets of extended uniqueness, among other thin sets) were studied on T and despite early accomplishments, the task of charac-terizing these sets remained an open problem. For a comprehensive source on sets of uniqueness of the circle, which is accompanied by several digres-sions on these difficulties, the reader is referred to [14]. In the 1950s, the subject regained additional vigour due to a functional-analytic reformula-tion of its language and in [5], the notion of (closed) set of uniqueness is extended to general locally compact groups relying on the framework of Fourier algebras, introduced in [9]. In the 1980s and 1990s, the incorpora-tion of descriptive set-theoretic methods in the study of sets of uniqueness (mostly in the abelian case) provided a deeper insight into some classical questions through the lens of a rather powerful language. In this paper we study some descriptive set-theoretic aspects-such as the descriptive com-plexity and (non-)existence of Borel basis-of closed sets of uniqueness in 2020 Mathematics Subject Classification: Primary 43A46; Secondary 03E15.
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| 9. |
- Persson, Tomas
(författare)
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A strong Borel–Cantelli lemma for recurrence
- 2023
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 268:1, s. 75-89
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Tidskriftsartikel (refereegranskat)abstract
- Consider a dynamical systems ([0, 1], T, µ) which is exponentially mixing for L1 against bounded variation. Given a non-summable sequence (mk) of non-negative numbers, one may define rk(x) such that µ(B(x, rk(x)) = mk. It is proved that for almost all x, the number of k ≤ n such that Tk(x) ∊ Bk(x) is approximately equal to m1+· · ·+mn. This is a sort of strong Borel–Cantelli lemma for recurrence. A consequence is that (Formula Presented) for almost every x, where τ is the return time.
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| 10. |
- Thiel, Hannes
(författare)
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Real rank of extensions of C *-algebras
- 2024
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Ingår i: STUDIA MATHEMATICA. - 0039-3223 .- 1730-6337.
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Tidskriftsartikel (refereegranskat)abstract
- Given a closed ideal A in a C * -algebra E, we develop techniques to bound the real rank of E in terms of the real ranks of A and E/A. Building on work of Brown, Lin and Zhang, we obtain explicit computations if A belongs to any of the following classes: (1) C * -algebras with real rank zero, stable rank one and vanishing K 1 -group; (2) simple, purely infinite C * -algebras; (3) simple, Z -stable C * -algebras with real rank zero; (4) separable, stable C * -algebras with an approximate unit of projections and the Corona Factorization Property.
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