Fourier analytic techniques in geometry and analysis

Search results

• 2026

  Assouad type dimensions of parabolic Julia sets

  Fraser, J. M. & Stuart, L., 1 Apr 2026, In: Mathematische Zeitschrift. 312, 4, 29 p., 108.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Parabolic 100%
  • Julia Set 100%
  • Assouad Dimension 66%
  • Hausdorff Dimension 33%
  • Box Dimension 16%

• Cover times in dynamical systems

  Jurga, N. & Todd, M., 6 Apr 2026, (E-pub ahead of print) In: Israel Journal of Mathematics. Online first, 60 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Dynamical System 100%
  • Wide Class 50%
  • Asymptotic Formula 50%
  • Gauss Map 50%

• The Hausdorff dimension of self-projective sets

  Christodoulou, A. & Jurga, N., 1 Jan 2026, In: Transactions of the American Mathematical Society. 379, 1, p. 1-32 32 p.

  Research output: Contribution to journal › Article › peer-review

  • Hausdorff Dimension 100%
  • Projective Set 100%
  • Iterated Function System 66%
  • Critical Exponent 33%
  • Projective 33%

• 2025

  Parabolic carpets

  Fraser, J. & Jurga, N. A., 20 Jan 2025, (E-pub ahead of print) In: Israel Journal of Mathematics. 39 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Parabolic 100%
  • Box Dimension 25%
  • Fixed Points 25%
  • Iterated Function System 25%
  • Gibbs Free Energy 25%

• 2024

  A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra

  Fraser, J. & Stuart, L., 1 Jan 2024, In: Bulletin of the American Mathematical Society. 61, 1, p. 103-118 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Parabolic 100%
  • Rational Map 100%
  • Julia Set 50%
  • Limit Set 50%
  • Hyperbolic Space 50%

• The Fourier spectrum and sumset type problems

  Fraser, J., 5 Apr 2024, In: Mathematische Annalen.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Hausdorff Dimension 100%
  • Convolution 100%
  • Set Satisfying 100%

• 2023

  A nonlinear projection theorem for Assouad dimension and applications

  Fraser, J., 1 Feb 2023, In: Journal of the London Mathematical Society. 107, 2, p. 777-797 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Projection Theorem 100%
  • Assouad Dimension 100%
  • Sharp Estimate 40%
  • Hausdorff Dimension 20%
  • Product Sum 20%

• Box dimensions of (×m,×n)-invariant sets

  Fraser, J. & Jurga, N. A., 1 Dec 2023, In: Indiana University Mathematics Journal. 72, 6, p. 2341-2367 27 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Invariant Set 100%
  • Subshift 83%
  • Upper Bound 33%
  • Lower and upper bounds 33%

• Dimensions of Kleinian orbital sets

  Bartlett, T. & Fraser, J., 6 Oct 2023, In: Journal of Fractal Geometry. 10, 3/4, p. 267-278 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Fractal 33%
  • Limit Set 33%
  • Hyperbolic Space 33%
  • Euclidean Space 33%

• Diophantine approximation in metric space

  Fraser, J., Koivusalo, H. & Ramirez, F., 1 Apr 2023, In: Bulletin of the London Mathematical Society. 55, 2, p. 756-776 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Diophantine Approximation 100%
  • Metric Space 100%
  • Real Number 33%

• Intermediate dimensions of infinitely generated attractors

  Banaji, A. & Fraser, J., 1 Apr 2023, In: Transactions of the American Mathematical Society. 376, 4, p. 2449-2479 31 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Limit Set 100%
  • Hausdorff Dimension 50%
  • Box Dimension 50%
  • Hausdorff 50%
  • Iterated Function System 50%

• Minkowski dimension for measures

  Falconer, K. J., Fraser, J. & Käenmäki, A., 1 Feb 2023, In: Proceedings of the American Mathematical Society. 151, 2, p. 779-794 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Minkowski Dimension 100%
  • Dimension Theory 66%
  • Box Dimension 33%
  • Compact Metric Space 33%

• Non-existence of the box dimension for dynamically invariant sets

  Jurga, N., 11 Dec 2023, In: Analysis & PDE. 16, 10, p. 2385-2399 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Invariant Set 100%
  • Nonexistence 100%
  • Hausdorff Dimension 33%
  • Hausdorff 16%

• On the convergence rate of the chaos game

  Bárány, B., Jurga, N. & Kolossváry, I., 1 Mar 2023, In: International Mathematics Research Notices. 2023, 5, p. 4456-4500 45 p., rnab370.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Minkowski Dimension 100%
  • Rate of Convergence 100%
  • Multiplicative 50%
  • Minimizes 50%
  • Probability Vector 50%

• Refined horoball counting and conformal measure for Kleinian group actions

  Fraser, J. & Stuart, L., 8 May 2023, In: Annales Academiae Scientiarum Fennicae-Mathematica. 48, 1, p. 325-344 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Parabolic 100%
  • Limit Set 75%
  • Fixed Points 50%
  • Pairwise Disjoint 25%
  • Countable Dense Subset 25%

• 2022

  Dimensions of the popcorn graph

  Chen, H., Fraser, J. & Yu, H., 18 Aug 2022, (E-pub ahead of print) In: Proceedings of the American Mathematical Society. 150, p. 4729-4742

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Diophantine Approximation 100%
  • Probability Theory 100%
  • Box Dimension 100%
  • Assouad Dimension 100%
  • Real Analysis 100%

• Ledrappier–Young formulae for a family of nonlinear attractors

  Lee, L. D. & Jurga, N. A., 1 Mar 2022, In: Mathematische Zeitschrift. 300, 3, p. 2413-2427 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Iterated Function System 100%
  • Invariant Measure 100%
  • Bernoulli Process 100%
  • Exact Dimension 100%
  • Gibbs Free Energy 100%

• On the Fourier dimension of (d,k)-sets and Kakeya sets with restricted directions

  Fraser, J., Harris, T. L. J. & Kroon, N. G., 24 Feb 2022, (E-pub ahead of print) In: Mathematische Zeitschrift. First Online, 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Unit Ball 100%
  • Hausdorff Dimension 50%

• The Assouad dimension of self-affine measures on sponges

  Fraser, J. & Kolossvary, I. T., 8 Sept 2022, (E-pub ahead of print) In: Ergodic Theory and Dynamical Systems. FirstView, 23 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Assouad Dimension 100%
  • Lower and upper bounds 40%
  • Explicit Formula 20%
  • Diagonalmatrix 20%

• The Assouad spectrum of Kleinian limit sets and Patterson-Sullivan measure

  Fraser, J. & Stuart, L., 10 Oct 2022, In: Geometriae Dedicata. 217, 32 p., 1.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Patterson 100%
  • Limit Set 100%
  • Assouad Dimension 100%
  • Hausdorff Dimension 25%

• The fractal structure of elliptical polynomial spirals

  Burrell, S. A., Falconer, K. J. & Fraser, J., 1 Sept 2022, In: Monatshefte für Mathematik. 199, p. 1-22

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Polynomial 100%
  • Fractal 100%
  • Spiral 100%
  • Fractional Brownian Motion 14%
  • Line Segment 14%

• 2021

  Approximate arithmetic structure in large sets of integers

  Fraser, J. & Yu, H., 2021, In: Real Analysis Exchange. 46, 1, p. 163-174

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Integer 100%
  • Approximates 100%
  • Arithmetic Progression 50%

• Assouad dimension influences the box and packing dimensions of orthogonal projections

  Falconer, K. J., Fraser, J. & Shmerkin, P., 2021, In: Journal of Fractal Geometry. 8, 3, p. 247–259

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Assouad Dimension 100%
  • Packing Dimension 100%
  • Orthogonal Projection 100%
  • Dimensional Subspace 20%

• Dimension spectrum of infinite self-affine iterated function systems

  Jurga, N. A., 16 Jun 2021, In: Selecta Mathematica: New Series. 27, 3, 23 p., 49.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Iterated Function System 100%
  • Isolated Point 20%
  • Real Number 20%

• How long is the chaos game?

  Morris, I. D. & Jurga, N., Dec 2021, In: Bulletin of the London Mathematical Society. 53, 6, p. 1749-1765 17 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Fractal 100%
  • Asymptotic Formula 33%
  • Open Set Condition 33%
  • Dense Subset 33%
  • Classical Theory 33%

• Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions

  Fraser, J., Shmerkin, P. & Yavicoli, A., 10 Feb 2021, In: Journal of Fourier Analysis and Applications. 27, 4, 14 p., 4.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Hausdorff Dimension 100%
  • Approximates 100%
  • Arithmetic Progression 100%
  • Box Dimension 50%
  • Supremum 50%

• L^q-spectra of measures on planar non-conformal attractors

  Falconer, K. J., Fraser, J. & Lee, L. D., Nov 2021, In: Ergodic Theory and Dynamical Systems. 41, 11, p. 3288-3306 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Iterated Function System 100%
  • Pressure Function 100%
  • Singular Value 100%
  • Lower Triangular Matrix 100%
  • Bernoulli Process 100%

• L^q-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums

  Fraser, J., Lee, L. D., Morris, I. D. & Yu, H., Sept 2021, In: Nonlinearity. 34, 9, p. 6331-6357 27 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Closed Form 100%
  • Counterexample 100%
  • Exponential Growth 25%
  • Diagonalmatrix 25%

• On Hölder maps and prime gaps

  Chen, H. & Fraser, J., 8 Nov 2021, In: Real Analysis Exchange. 46, 2, p. 523-532

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Positive Integer 100%
  • Hlder Continuity 100%

• On Hölder solutions to the spiral winding problem

  Fraser, J., 7 May 2021, In: Nonlinearity. 34, 5, p. 3251–3270 20 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Spiral 100%
  • Polynomial 33%
  • Box Dimension 16%
  • Line Segment 16%
  • Dimension Theory 16%

• Projection theorems for intermediate dimensions

  Burrell, S. A., Falconer, K. J. & Fraser, J. M., 1 May 2021, In: Journal of Fractal Geometry. 8, 2, p. 95-116 22 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Hausdorff Dimension 100%
  • Fractal 100%
  • Hausdorff 100%
  • Projection Theorem 100%
  • Box-Counting Dimension 100%

• Regularity versus smoothness of measures

  Fraser, J. & Troscheit, S., 31 Jul 2021, In: Pacific Journal of Mathematics. 311, 2, p. 257–275 17 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Regular Measure 100%
  • Continuous Measure 100%

• The box dimensions of exceptional self-affine sets in ℝ3

  Fraser, J. & Jurga, N. A., 16 Jul 2021, In: Advances in Mathematics. 385, 32 p., 107734.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Self-Affine Set 100%
  • Box Dimension 100%
  • Multiplicative 33%
  • Self-Similar Set 33%
  • Singular Value 33%

• 2020

  Intermediate dimensions

  Falconer, K. J., Fraser, J. & Kempton, T. M. W., Oct 2020, In: Mathematische Zeitschrift. 296, 1-2, p. 813–830 18 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Hausdorff Dimension 100%
  • Box Dimension 66%
  • Integer 33%
  • Negative Power 33%
  • Distribution Mass 33%

• Schmidt's game on Hausdorff metric and function spaces: generic dimension of sets and images

  Farkas, Á., Fraser, J., Nesharim, E. & Simmons, D., 29 Dec 2020, In: Mathematika. 67, 1, p. 196-213

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Metric Space 100%
  • Function Space 100%
  • Hausdorff Metric 100%
  • Residuals 33%
  • Compact Subset 33%

• The Assouad spectrum of random self-affine carpets

  Fraser, J. & Troscheit, S., 15 Oct 2020, (E-pub ahead of print) In: Ergodic Theory and Dynamical Systems. First View, 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Assouad Dimension 100%
  • Box Dimension 40%
  • Random Model 20%
  • Random Variable 20%

• The dimensions of inhomogeneous self-affine sets

  Burrell, S. A. & Fraser, J. M., 2020, In: Annales Academiae Scientiarum Fennicae-Mathematica. 45, 1, 313-324.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Self-Affine Set 100%
  • Box Dimension 33%
  • Upper Bound 33%
  • Sufficient Condition 33%

• 2019

  Almost arithmetic progressions in the primes and other large sets

  Fraser, J. M., May 2019, In: The American Mathematical Monthly. 126, 6, p. 553-558 6 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Arithmetic Progression 100%

• On the Hausdorff dimension of microsets

  Fraser, J. M., Howroyd, D. C., Käenmäki, A. & Yu, H., Nov 2019, In: Proceedings of the American Mathematical Society. 147, 11, p. 4921-4936 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Hausdorff Dimension 100%
  • Supremum 33%
  • Infimum 33%
  • Assouad Dimension 33%
  • Maximal Dimension 33%

• Regularity of Kleinian limit sets and Patterson-Sullivan measures

  Fraser, J. M., 1 Oct 2019, In: Transactions of the American Mathematical Society. 372, 7, p. 4977-5009 33 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Patterson 100%
  • Limit Set 100%
  • Hausdorff 33%
  • Box-Counting Dimension 33%

• The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra

  Fraser, J. M., Hare, K. E., Hare, K. G., Troscheit, S. & Yu, H., 17 Jan 2019, In: Annales Academiae Scientiarum Fennicae-Mathematica. 44, 1, p. 379-387

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Assouad Dimension 100%
  • Box-Counting Dimension 50%

• 2018

  Dimension growth for iterated sumsets

  Fraser, J., Howroyd, D. C. & Yu, H., 17 Dec 2018, (E-pub ahead of print) In: Mathematische Zeitschrift. First Online, 28 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Box Dimension 100%
  • Perfect Set 100%
  • Semigroup 100%
  • Entropy 100%