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GRA:020117Mathematical problem title

Gra2 Centered Hardy Littlewood MaximalGra2 Weak Type Level Set Measure

Differentiation of measures and absolute continuityGraduate Real Analysis II · Mixed review

GRA:020218Mathematical problem title

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Gra2 Fourier Convolution TheoremGra2 Plancherel Sinc Fourth

Fourier transform and convolutionGraduate Real Analysis II · Mixed review

GRA:020219Mathematical problem title

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Gra2 Beta Function Singular KernelGra2 Truncated Convolution Limits

Fourier transform and convolutionGraduate Real Analysis II · Mixed review

GRA:020220Mathematical problem title

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Gra2 Integration BY Parts FourierGra2 Fourier Decay From Jumps

Fourier transform and convolutionGraduate Real Analysis II · Mixed review

GRA:020221Mathematical problem title

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Gra2 Principal Value HilbertGra2 Hilbert L2 Isometry

Fourier transform and convolutionGraduate Real Analysis II · Mixed review

GRA:020322Mathematical problem title

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Graduate Real Analysis 2 Box Mollified CuspGraduate Real Analysis 2 Mollifier C1 Not C2

Approximate identities and densityGraduate Real Analysis II · Mixed review

GRA:020325Mathematical problem title

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Graduate Real Analysis 2 L2 Tail TruncationGraduate Real Analysis 2 L2 Not L1 Halfline

Approximate identities and densityGraduate Real Analysis II · Mixed review

GRA:020423Mathematical problem title

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Graduate Real Analysis 2 Oscillatory Square Weak LimitGraduate Real Analysis 2 Weak Limit Nonlinear

Weak convergence of functions and measuresGraduate Real Analysis II · Mixed review

GRA:020426Mathematical problem title

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Graduate Real Analysis 2 X Power Weak StarGraduate Real Analysis 2 Weak Star Versus Norm

Weak convergence of functions and measuresGraduate Real Analysis II · Mixed review

GRA:020524Mathematical problem title

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Graduate Real Analysis 2 Dirichlet Poincare LedgerGraduate Real Analysis 2 Rayleigh Quotient Polynomial

Distributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed review

GRA:020527Mathematical problem title

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Gra2 Translated Delta Testing PairingGra2 Tempered Fourier Multiplier Phase

Distributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed review

GRA:020528Mathematical problem title

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Gra2 Gagliardo Seminorm IndicatorGra2 Fractional Sobolev Threshold

Distributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed review

GRA:020529Mathematical problem title

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Gra2 Lacunary Fourier SeriesGra2 Sobolev HS Threshold Torus

Distributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed review

GRA:020630Mathematical problem title

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Gra2 Weak Convergence Bounded ContinuousGra2 Wasserstein One Gap

Probability measures, tightness, and convergence in lawGraduate Real Analysis II · Mixed review

GRA:020631Mathematical problem title

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Gra2 Empirical Quantile CouplingGra2 Wasserstein One Rate

Probability measures, tightness, and convergence in lawGraduate Real Analysis II · Mixed review

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GRA:020117Mathematical problem title

GRA:020218Mathematical problem title

GRA:020219Mathematical problem title

GRA:020220Mathematical problem title

GRA:020221Mathematical problem title

GRA:020322Mathematical problem title

GRA:020325Mathematical problem title

GRA:020423Mathematical problem title

GRA:020426Mathematical problem title

GRA:020524Mathematical problem title

GRA:020527Mathematical problem title

GRA:020528Mathematical problem title

GRA:020529Mathematical problem title

GRA:020630Mathematical problem title

GRA:020631Mathematical problem title

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Problem results

GRA:020117The centered maximal function of 1_[0,1] has a three-unit quarter-level set, not a doubled-interval guessMathematical problem title

GRA:020218A triangular hat transforms to sinc squared and Plancherel makes sinc fourth integrate to 2/3Mathematical problem title

GRA:020219Two integrable endpoint singularities convolve to a pi plateau before the arcsine tailMathematical problem title

GRA:020220A boundary jump leaves a one-over-k Fourier tail even when the interior derivative is harmlessMathematical problem title

GRA:020221The Hilbert transform of an interval indicator is logarithmic, odd, and still L2Mathematical problem title

GRA:020322A symmetric box average rounds the absolute-value cusp by exactly epsilon over twoMathematical problem title

GRA:020325Compact truncation reaches an L2 tail at an exact rate while the same function never enters L1Mathematical problem title

GRA:020423Weak convergence does not commute with squaring: sqrt(2) sin(2 pi n x) vanishes while its energy tends to oneMathematical problem title

GRA:020426The powers x^n are weak-star null in L-infinity while their supremum norm never movesMathematical problem title

GRA:020524The polynomial x(1-x) passes the sharp Dirichlet Poincare inequality with quotient one tenthMathematical problem title

GRA:020527A translated delta derivative carries a testing minus sign, a Fourier multiplier, and a phaseMathematical problem title

GRA:020528An interval indicator belongs to fractional H^s exactly below one half, with a computable Gagliardo blow-upMathematical problem title

GRA:020529A lacunary Fourier tail has unit L2 mass and dies at the H one-half endpointMathematical problem title

GRA:020630Vanishing escaping mass converges weakly but stays exactly one unit away in Wasserstein oneMathematical problem title

GRA:020631Right-endpoint empirical mass approximates the uniform law at exact Wasserstein rate one over two nMathematical problem title

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GRA:020117Mathematical problem titleView problem statement

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Problem results

GRA:020117The centered maximal function of 1_[0,1] has a three-unit quarter-level set, not a doubled-interval guessMathematical problem titleView problem statement

GRA:020117Mathematical problem title

GRA:020117The centered maximal function of 1_[0,1] has a three-unit quarter-level set, not a doubled-interval guessMathematical problem title