Project MUSE®: American Journal of Mathematics - Latest Articles
https://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in American Journal of Mathematics.daily12026-05-19T00:00:00-05:00text/htmlen-USVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®Multiresolution analysis and Zygmund dilations
https://muse.jhu.edu/article/986595
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Zygmund dilations are a group of dilations lying in between the standard product theory and the one-parameter setting – in ℝ3 = ℝ × ℝ × ℝ they are the dilations (x1, x2, x3) ↦ (δ1x1, δ2x2, δ1δ2x3). The dyadic multiresolution analysis and the related dyadic-probabilistic methods have been very impactful in the modern product singular integral theory. However, multiresolution analysis has not been understood in the Zygmund dilation setting or in other modified product space settings. In this paper we develop this missing dyadic multiresolution analysis of Zygmund type, and justify its usefulness by bounding, on weighted spaces, a general class of singular integrals that are invariant under Zygmund dilations. We
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallMultiresolution analysis and Zygmund dilations2026-03-31text/htmlen-USMultiresolution analysis and Zygmund dilations2026-03-312026TWOProject MUSE®261532026-05-19T00:00:00-05:002026-03-31An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications
https://muse.jhu.edu/article/986596
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Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional p-adic Lie extension whose Galois group has an abelian Sylow p-subgroup. Crucially, this result does not depend on the vanishing of any µ-invariant. As applications, we deduce the Coates–Sinnott conjecture away from its 2-primary part and new cases of the equivariant Tamagawa number conjecture for Tate
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallAn unconditional proof of the abelian equivariant Iwasawa main conjecture and applications2026-03-31text/htmlen-USAn unconditional proof of the abelian equivariant Iwasawa main conjecture and applications2026-03-312026TWOProject MUSE®565762026-05-19T00:00:00-05:002026-03-31On the first sign change of Fourier coefficients of cusp forms
https://muse.jhu.edu/article/986597
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We present a variant of the current widely-used method initiated by Choie and Kohnen in the study of the location of the first sign change of the Fourier coefficients of a holomorphic cusp form when all the coefficients are real. This version circumvents the use of Atkin-Lehner theory of cuspidal newforms, instead utilizing the Eisenstein series, and it applies directly to cases including integral weight cusp forms on the congruence subgroup Γ0(N) of any level N as well as half-integral weight cusp
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallOn the first sign change of Fourier coefficients of cusp forms2026-03-31text/htmlen-USOn the first sign change of Fourier coefficients of cusp forms2026-03-312026TWOProject MUSE®206712026-05-19T00:00:00-05:002026-03-31Simultaneous dilation and translation tilings of ℝn
https://muse.jhu.edu/article/986598
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We solve the wavelet set existence problem. That is, we characterize the full-rank lattices Γ ⊂ ℝn and invertible n×n matrices A for which there exists a measurable set W such that {W + γ : γ ∈ Γ} and {Aj (W) : j ∈ ℤ} are tilings of ℝn. The characterization is a non-obvious generalization of the one found by Ionascu and Wang (2006), which solved the problem in the case n = 2. As an application of our condition and a theorem of Margulis, we also strengthen a result of Dai, Larson, and the second author on the existence of wavelet sets by showing that wavelet sets exist for matrix dilations, all of whose eigenvalues λ satisfy |λ| ≥ 1. As another application, we extend the Ionascu-Wang characterization to higher
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallSimultaneous dilation and translation tilings of ℝn2026-03-31text/htmlen-USSimultaneous dilation and translation tilings of ℝn2026-03-312026TWOProject MUSE®247982026-05-19T00:00:00-05:002026-03-31Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces
https://muse.jhu.edu/article/986599
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We establish Lipschitz regularity of harmonic maps from RCD(K,N) metric measure spaces with lower Ricci curvature bounds and dimension upper bounds in synthetic sense with values into CAT(0) metric spaces with non-positive sectional curvature. Under the same assumptions, we obtain a Bochner-Eells-Sampson inequality with a Hessian type-term. This gives a fairly complete generalization of the classical theory for smooth source and target spaces to their natural synthetic counterparts and an affirmative answer to a question raised several times in the recent literature.The proofs build on a new interpretation of the interplay between Optimal Transport and the Heat Flow on the source space and on an original
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallLipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces2026-03-31text/htmlen-USLipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces2026-03-312026TWOProject MUSE®811492026-05-19T00:00:00-05:002026-03-31m-point correlations of the fractional parts of αnθ
https://muse.jhu.edu/article/986600
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Let m ≥ 3, we prove that (αnθ mod 1)n>0 has Poissonian m-point correlation for all α > 0, provided θ < θm, where θm is an explicit bound which goes to 0 as m increases. This work builds on the method developed in Lutsko-Sourmelidis-Technau (2021), and introduces a new combinatorial argument for higher correlation levels, and new Fourier analytic techniques. A key point is to introduce an 'extra' frequency variable to de-correlate the sequence variables and to eventually exploit a repulsion principle for oscillatory integrals. Presently, this is the only positive result showing that the m-point correlation is Poissonian for such
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallm-point correlations of the fractional parts of αnθ2026-03-31text/htmlen-USm-point correlations of the fractional parts of αnθ2026-03-312026TWOProject MUSE®238752026-05-19T00:00:00-05:002026-03-31Inertia groups in the metastable range
https://muse.jhu.edu/article/986601
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We prove that the inertia groups of all sufficiently-connected, high-dimensional (2n)-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for m ≫ 0 and k > 5/12, suppose M is a ⌊km⌋-connected, smooth, closed, oriented m-manifold and Σ is an exotic m-sphere. We prove that, if M♯Σ is diffeomorphic to M, then Σ bounds a parallelizable manifold. Our proof is built on an understanding of the second extended power functor in Pstrągowski's category of synthetic
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Project MUSE®https://muse.jhu.edu/2026-05-19T00:00:00-05:00https://muse.jhu.edu/journal/5/image/coversmallInertia groups in the metastable range2026-03-31text/htmlen-USInertia groups in the metastable range2026-03-312026TWOProject MUSE®366292026-05-19T00:00:00-05:002026-03-31