1,720,966 research outputs found
Extension operators for smooth functions on compact subsets of the reals
Get PDF[EN] We introduce sufficient as well as necessary conditions for a compact set K such that there is a continuous linear extension operator from the space of restrictions C-infinity (K) = {F vertical bar(K) : F is an element of C-infinity (R)} to C-infinity (R). This allows us to deal with examples of the form K = {a(n) : n is an element of N} boolean OR{0} for a(n) -> 0 previously considered by Fefferman and Ricci as well as Vogt.The research of all authors was partially supported by GVA AICO/2016/054 . The
research of the second author was partially supported by the project MTM2016-76647-P.Frerick, L.; Jorda Mora, E.; Wengenroth, J. (2020). Extension operators for smooth functions on compact subsets of the reals. Mathematische Zeitschrift. 295(3-4):1537-1552. https://doi.org/10.1007/s00209-019-02388-5S153715522953-4Bos, Len P., Milman, Pierre D.: Sobolev–Gagliardo–Nirenberg and Markov type inequalities on subanalytic domains. Geom. Funct. Anal. 5(6), 853–923 (1995)Bierstone, Edward, Milman, Pierre D.: Geometric and differential properties of subanalytic sets. Ann. Math. (2) 147(3), 731–785 (1998)Bierstone, Edward, Milman, Pierre D., Pawłucki, Wiesław: Composite differentiable functions. Duke Math. J. 83(3), 607–620 (1996)DeVore, Ronald A., Lorentz, George G.: Constructive approximation, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 303. Springer, Berlin (1993)Fefferman, Charles: extension by linear operators. Ann. Math. (2) 166(3), 779–835 (2007)Frerick, Leonhard, Jordá, Enrique, Wengenroth, Jochen: Tame linear extension operators for smooth Whitney functions. J. Funct. Anal. 261(3), 591–603 (2011)Frerick, Leonhard, Jordá, Enrique, Wengenroth, Jochen: Whitney extension operators without loss of derivatives. Rev. Mat. Iberoam. 32(2), 377–390 (2016)Fefferman, Charles, Ricci, Fulvio: Some examples of extension by linear operators. Rev. Mat. Iberoam. 28(1), 297–304 (2012)Frerick, Leonhard: Extension operators for spaces of infinite differentiable Whitney jets. J. Reine Angew. Math. 602, 123–154 (2007)Goncharov, Alexander: A compact set without Markov’s property but with an extension operator for -functions. Studia Math. 119(1), 27–35 (1996)Hörmander, Lars: The analysis of linear partial differential operators. I, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer, Berlin, Distribution theory and Fourier analysis (1990)Malgrange, Bernard: Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, (1967)Merrien, Jean: Prolongateurs de fonctions différentiables d’une variable réelle. J. Math. Pures Appl. (9) 45, 291–309 (1966)Mitjagin, B.S.: Approximate dimension and bases in nuclear spaces. Uspehi Mat. Nauk 16(4 (100)), 63–132 (1961)Meise, Reinhold, Vogt, Dietmar: Introduction to functional analysis, Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press, Oxford University Press, New York (1997). Translated from the German by M. S. Ramanujan and revised by the authorsPawłucki, Wiesław: On the algebra of functions -extendable for each finite. Proc. Am. Math. Soc. 133(2), 481–484 (2005). (Electronic)Pawłucki, Wiesław, Pleśniak, Wiesław: Extension of functions from sets with polynomial cusps. Studia Math. 88(3), 279–287 (1988)Stein, Elias M.: Singular integrals and differentiability properties of functions, Princeton Mathematical Series, vol. 30. Princeton University Press, Princeton (1970)Tidten, Michael: Fortsetzungen von -Funktionen, welche auf einer abgeschlossenen Menge in definiert sind. Manuscripta Math. 27(3), 291–312 (1979)Vogt, Dietmar: Restriction spaces of . Rev. Mat. Iberoam. 30(1), 65–78 (2014)Vogt, Dietmar, Wagner, Max Josef: Charakterisierung der Quotientenräume von und eine Vermutung von Martineau. Studia Math. 67(3), 225–240 (1980)Wengenroth, Jochen: Derived functors in functional analysis. Lecture Notes in Mathematics, vol. 1810. Springer, Berlin (2003)Whitney, Hassler: Analytic extensions of differentiable functions defined in closed sets. Trans. Am. Math. Soc. 36(1), 63–89 (1934)Whitney, Hassler: On ideals of differentiable functions. Am. J. Math. 70, 635–658 (1948
Surjectivity of partial differential operators with good fundamental solutions
No full textAbstractWe characterize the surjectivity of a linear partial differential operator with constant coefficients on E(Ω) as well as on D′(Ω) in terms of the existence of “good” shifted fundamental solutions. This characterization complements results of Meise, Taylor, and Vogt as well as Frerick and the present author
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Acyclic inductive spectra of Fréchet spaces
No full textWe provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970.
For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem whether regular (LF)-spaces are complete has a positive solution in this case and we show that even the weakest regularity conditions already imply acyclicity.
One of the main benefits from our results is an improvement in the theory of projective spectra of (DFM)-spaces. We prove the missing implication in a theorem of Vogt and thus obtain evaluable conditions for vanishing of the derived projective limit functor which have direct applications to classical problems of analysis like surjectivity of partial differential operators on various classes of ultradifferentiable functions (as was explained e.g. by Braun, Meise and Vogt)
A conjecture of Palamodov about the functors Extk in the category of locally convex spaces
No full textAbstractIn 1971 Palamodov proved that in the category of locally convex spaces the derived functors Extk(E,X) of Hom(E,·) all vanish if E is a (DF)-space, X is a Fréchet space, and one of them is nuclear. He conjectured a “dual result”, namely that Extk(E,X)=0 for all k∈N if E is a metrizable locally convex space, X is a complete (DF)-space, and one of them is nuclear. Assuming the continuum hypothesis we give a complete answer to this conjecture: If X is an infinite-dimensional nuclear (DF)-space, then (1)There is a normed space E such that Ext1(E,X)≠0.(2)Ext2(KN,X)≠0 where KN is a countable product of lines.(3)Extk(E,X)=0 for all k⩾3 and all locally convex spaces E
Derived functors in functional analysis
No full textThe text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators. The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
