Hausdorff-young inequality
WebMay 30, 2024 · In this paper, we prove several important sharp inequalities, including the Hausdorff-Young inequality and its converse, Pitt's inequality and Lieb's inequality for Clifford ambiguity functions. http://helper.ipam.ucla.edu/publications/ccgws3/ccgws3_11829.pdf
Hausdorff-young inequality
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It has been shown in the first section that the Fourier transform maps L (R ) boundedly into L (R ) and L (R ) into itself. A similar argument shows that the Fourier series operator, which transforms periodic functions f : T → C into functions whose values are the Fourier coefficients The Hausdorff–Young inequality can also be established for the Fourier transform on locally compact Abelian groups. The norm estimate of 1 is not optimal. See the main article for references. WebJan 9, 2024 · The sharp local central Hausdorff–Young inequality for arbitrary compact Lie groups (Theorem 1.4) is proved in Sect. 4; to better explain the underlying idea without delving into technicalities, the proof of the abelian case (Theorem 1.2) is …
WebIn Q5, the good lambda inequality should require f^# to be less than eps lambda, rather than greater than eps lambda. ... Young’s inequality, Hausdorff-Young, Christ-Kiselev. (updated, Dec 6. Erratum, Dec 23 2024: In the definition of f (and its Fourier transform) on page 21, a factor of exp( -pi i n^2 v ^2) should be added.) WebTogether with the Plancherel identity and Hausdorff–Young inequality, we establish Lp(R2) multiplier theory and Littlewood–Paley theorems associated with the 2D-LCT. As applications, we demonstrate the recovery of the L1(R2) signal function by simulation. Moreover, we present a real-life application of such a theory of 2D-LCT by encrypting ...
WebAbstract. This note describes two results: ( i) a sharp Hausdorff-Young inequality for the Fourier transform on Lp ( Rn) which extends an earlier result of Babenko; and ( ii) a … WebJun 4, 2014 · The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space …
WebReverse Hausdorff Young for nonnegative functions. Asked 8 years, 4 months ago. Modified 8 years, 4 months ago. Viewed 1k times. 6. The classical Hausdorff-Young inequality states that. ‖ f ^ ‖ p ′ ≤ ‖ f ‖ p for 1 ≤ p ≤ 2. For p = 2, we even have equality due to Plancherel. If we additionally assume that f ≥ 0, we also get.
WebMay 1, 2024 · The Hausdorff–Young inequality is a bound on the norm M p = F L p → L q, where q = p / (p − 1). Hirschman discovered that differentiating M p gives an uncertainty principle for the Shannon entropy, generalizing the well-known Heisenberg principle. size of phono plug and mini plugWebJun 18, 2015 · Hausdorff-Young inequality on torus. 1. Inverse Hausdorff Young. 0. Understanding the proof of the Hausdorff-Young theorem. 1. Does the Hausdorff-Young inequality hold on bounded sets? 1. Hausdorff–Young inequality. 2. Interpolation inequality of fourier transformation. Hot Network Questions sustained od feeWebApr 15, 2024 · Sharp Hausdorff-Young inequality. The sharp Hausdorff-Young inequality plays an important role in Harmonic analysis. However, even for the two-sided quaternion Fourier transform, the sharp Hausdorff-Young inequalities has been overlooked for many years, which was only achieved recently by the symplectic decomposition of … sustained opinion definition<2$, and further … size of phoenix azWebintegral operators on L2(Rn)[22], and an inequality of Hausdorff–Young type can be proved for ρ [38,57]: for all p ∈[1,2], ρ(f) Sp L(L2 Rn)) ≤ C f p(Cn), (1.3) where … sustained objection definition lawWebA HAUSDORFF{YOUNG INEQUALITY FOR LOCALLY COMPACT QUANTUM GROUPS TOM COONEY Abstract. Let G be a locally compact abelian group with dual group G^. The Hausdor {Young theorem states that if f 2Lp(G), where 1 p 2, then its Fourier transform Fp(f) belongs to Lq(G^) (where 1 p + 1 q = 1) and jjFp(f)jjq jjfjjp. Kunze and Terp extended this … sustained off resonance irradiationWebThis paper studies Banach space valued Hausdorff-Young inequalities. The largest part considers ways of changing the underlying group. In particular the possibility to deduce the inequality for open subgroups as well as for quotient groups arising from compact subgroups is secured. A large body of results concerns the classical groupsT n ,R n … sustained objection meaning