1,720,956 research outputs found
Non-homogeneous strongly singular integrals
No full textWe study the Lp mapping properties of a family of strongly singular oscillatory integral operators on ℝn which are non-homogeneous in the sense that their kernels have isotropic oscillations but non-isotropic singularities. © Instytut Matematyczny PAN, 2008.ABIKHUZAM F, 2001, J MATH ANAL APPL, V50, P1015; FEFFERMA.C, 1972, ACTA MATH-UPPSALA, V129, P137, DOI 10.1007-BF02392215; FEFFERMA.C, 1970, ACTA MATH-UPPSALA, V124, P9, DOI 10.1007-BF02394567; LYALL N, T AM MATH S IN PRESS; Shayya B, 2001, INDIANA U MATH J, V50, P1015; Shayya B, 2002, T AM MATH SOC, V354, P4893, DOI 10.1090-S0002-9947-02-03097-0; SJOLIN P, 1979, MATH Z, V165, P231, DOI 10.1007-BF01437558; SJOLIN P, 1976, ARK MAT, V14, P59, DOI 10.1007-BF02385824; SJOLIN P, 1981, INDIANA U MATH J, V30, P47, DOI 10.1512-iumj.1981.30.30004; Stein E., 1993, HARMONIC ANAL REAL V; STEIN EM, 1978, B AM MATH SOC, V84, P1239, DOI 10.1090-S0002-9904-1978-14554-6; Wainger S., 1965, MEM AM MATH SOC, V590
Affine restriction for radial surfaces
No full textSuppose dμ is affine surface measure on a convex radial surface Γ(x) = (x, γ ([pipe]x[pipe])), a ≤ [pipe]x[pipe] andlt; b, in ℝ3. Under appropriate smoothness and growth conditions on γ, we prove (L4-3(ℝ3), L4-3(dμ)) and (L4-3(ℝ3), L2(dμ)) Fourier restriction estimates for Γ. © Springer-Verlag 2008.Abi-Khuzam F, 2006, PUBL MAT, V50, P71; Aleksandrov A.D., 1939, UCHENYE ZAPISKI LENI, V6, P3; Carbery A, 2002, PUBL MAT, V46, P405; Carbery A, 2007, P AM MATH SOC, V135, P1905, DOI 10.1090-S0002-9939-07-08689-3; DOLZMANN G, 1995, ARCH MATH, V65, P352, DOI 10.1007-BF01195547; Federer H., 1996, GEOMETRIC MEASURE TH; GREENLEAF A, 1981, INDIANA U MATH J, V30, P519, DOI 10.1512-iumj.1981.30.30043; Hug D, 1996, MANUSCRIPTA MATH, V91, P283, DOI 10.1007-BF02567955; Iosevich A, 2000, CAN MATH BULL, V43, P63, DOI 10.4153-CMB-2000-009-7; Iosevich A, 1999, B UNIONE MAT ITAL, V2B, P383; Ludwig M, 1999, ADV MATH, V147, P138, DOI 10.1006-aima.1999.1832; LUTWAK E, 1991, ADV MATH, V85, P39, DOI 10.1016-0001-8708(91)90049-D; Oberlin DM, 2001, P AM MATH SOC, V129, P3303, DOI 10.1090-S0002-9939-01-06012-9; Oberlin DM, 1999, P AM MATH SOC, V127, P3591, DOI 10.1090-S0002-9939-99-05462-3; Oberlin DM, 2004, P AM MATH SOC, V132, P3195, DOI 10.1090-S0002-9939-04-07610-5; Oberlin DM, 2004, P AM MATH SOC, V132, P1195, DOI 10.1090-S0002-9939-03-07289-7; SCHUTT C, 1993, P AM MATH SOC, V118, P1213, DOI 10.2307-2160080; SCHUTT C, 1990, MATH SCAND, V66, P275; Shayya B, 2007, P AM MATH SOC, V135, P1107, DOI 10.1090-S0002-9939-06-08604-7; SJOLIN P, 1974, STUD MATH, V51, P169; Stein E., 1993, HARMONIC ANAL REAL V11
When the cone in Bochner's theorem has an opening less than π
No full textWe prove that if the Fourier transform of a measure μ ∈ M(ℝ n) vanishes in the interior of a cone of opening less than π, then the distance set [|x-τ|: x∈G∩supp μ has a positive one-dimensional Lebesgue measure whenever τ ∈ ℝ n, G⊂ ℝ n is open, and μ(G)≠0. When the cone has an opening greater than π, it is well known that μ is absolutely continuous with respect to Lebesgue measure on ℝ n. For measures on the n-torus, this dates back to a 1944 paper of Bochner. For measures on ℝ n, this follows from a Euclidean space version of Forelli's theorem about analytic and quasi-invariant measures. Forelli's theorem was proved in a 1967 paper in the abstract setting of a locally compact Hausdorff space on which ℝ acts as a topological transformation group. We give a Euclidean space proof of this Euclidean space version of Forelli's theorem. © 2011 London Mathematical Society.Bochner S, 1944, ANN MATH, V45, P708, DOI 10.2307-1969298; DELEEUW K, 1963, ACTA MATH-DJURSHOLM, V109, P179; Erdogan MB, 2005, INT MATH RES NOTICES, P1411; FORELLI F, 1967, ACTA MATH-UPPSALA, V118, P33, DOI 10.1007-BF02392475; HELSON H, 1958, ACTA MATH-DJURSHOLM, V99, P165, DOI 10.1007-BF02392425; MATTILA P, 1987, MATHEMATIKA, V34, P207; Peres Y, 2000, DUKE MATH J, V102, P193; Shayya B, 2011, CAN MATH BULL, V54, P172, DOI 10.4153-CMB-2010-077-2; Stein E., 1993, HARMONIC ANAL REAL V; Wolff T, 1999, INT MATH RES NOTICES, P547; Wolff T. H., 2003, U LECT SERIES, V290
An affine restriction estimate in R3
No full textWe prove that the Fourier transform of an L4-3 function can be restricted to any compact convex C2 surface of revolution in R 3. © 2006 American Mathematical Society.Abi-Khuzam F, 2006, PUBL MAT, V50, P71; Aleksandrov A.D., 1939, UCHENYE ZAPISKI LENI, V6, P3; DOLZMANN G, 1995, ARCH MATH, V65, P352, DOI 10.1007-BF01195547; Hug D, 1996, MANUSCRIPTA MATH, V91, P283, DOI 10.1007-BF02567955; Ludwig M, 1999, ADV MATH, V147, P138, DOI 10.1006-aima.1999.1832; LUTWAK E, 1991, ADV MATH, V85, P39, DOI 10.1016-0001-8708(91)90049-D; Oberlin DM, 2001, P AM MATH SOC, V129, P3303, DOI 10.1090-S0002-9939-01-06012-9; Oberlin DM, 2004, P AM MATH SOC, V132, P3195, DOI 10.1090-S0002-9939-04-07610-5; Oberlin DM, 2004, P AM MATH SOC, V132, P1195, DOI 10.1090-S0002-9939-03-07289-7; SCHUTT C, 1993, P AM MATH SOC, V118, P1213, DOI 10.2307-2160080; SCHUTT C, 1990, MATH SCAND, V66, P275; SJOLIN P, 1974, STUD MATH, V51, P16977
Adjoint restriction estimates and scaling on spheres
No full textWe test the restriction conjecture, in its adjoint form, against a class of measures φδdσ on the sphere Sn-1. The densities φδ are smoothed out characteristic functions of δa2 × δa3 × ⋯ × δan rectangular caps on Sn-1, where a 2,a3, . . ., an are fixed nonnegative numbers.BECKNER W, 1989, B LOND MATH SOC, V21, P394, DOI 10.1112-blms-21.4.394; Stein E., 1993, HARMONIC ANAL REAL V; TOMAS PA, 1975, B AM MATH SOC, V81, P477, DOI 10.1090-S0002-9904-1975-13790-60
Measures with Fourier Transforms in <i>L</i><sup>2</sup> of a Half-space
No full textAbstractWe prove that if the Fourier transform of a compactly supported measure is in L2 of a half-space, then the measure is absolutely continuous to Lebesgue measure. We then show how this result can be used to translate information about the dimensionality of a measure and the decay of its Fourier transform into geometric information about its support.</jats:p
Fourier restriction to convex surfaces of revolution in ℝ3
No full textIf F is a C3 hypersurface in ℝn and dσ is induced Lebesgue measure on Γ, then it is well known that a Tomas-Stein Fourier restriction estimate on Γ implies that Γ has a nowhere vanishing Gaussian curvature. In a recent paper, Carbery and Ziesler observed that if induced Lebesgue measure is replaced by affine surface area, then a Tomas-Stein restriction estimate on Γ implies that Γ satisfies the affine isoperimetric inequality. Since the only property needed for a hypersurface to satisfy the affine isoperimetric inequality is convexity, this raised the question of whether a Tomas-Stein restriction estimate can be obtained for flat but convex hypersurfaces in ℝn such as Γ(x) = (x, e-1-|x|m), m = 1,2, . . . . We prove that this is indeed the case in dimension n = 3.
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
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