Kathryn E. Hare

Contact information

Department of Pure Mathematics 
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1

Email: kehare@uwaterloo.ca

Curriculum Vitae

Degrees

• PhD (University of British Columbia) 1986

• BMath (University of Waterloo) 1981

Awards

• Fellow Canadian Mathematical Society, 2020

• University of Waterloo, Mathematics Faculty Distinction in Teaching Award, 2020

• Honourary Doctorate of Technology, Chalmers University of Technology, 2011

• Female Guest Professor, Sweden, 2000-2001

• AMS Featured Review, 1995

• NSERC Postgraduate Scholarship, 1983-85

• I.W. Killam Predoctoral Fellowship, 1985-86

• NSERC Operating Grant, 1987-date

Academic appointments

University of Waterloo administrative appointments

Selected External service

Research papers

Papers in refereed journals

(a) Harmonic analysis on compact Lie groups

• K. Hare and S. Gupta, Smoothness of convolutions of orbital measures on complex Grassmannians, accepted by J. Lie Theory.
• K. Hare and S. Gupta, Transferring spherical multipliers on compact symmetric spaces, accepted by Math Zeitschrift.
• K. Hare and J. He, Geometric proof of the L2 - singular dichotomy for orbital measures on Lie algebras and groups, Boll. Unione Mat. Ital. 11(2018), 573–580.
• K. Hare and S. Gupta, The absolute continuity of convolutions of orbital measures in symmetric spaces, J. Math. Anal. and Appl. 450(2017), 81–111.
• K. Hare and J. He, The absolute continuity of convolution products of orbital measures in symmetric spaces, Monatsh. Math. 182(2017), 619–635.
• K. Hare and J. He, Smoothness of convolution products of orbital measures on rank one symmetric spaces, Bull. Aust. Math. Soc. 94(2016), 131–143.
• K. Hare and S. Gupta, Characterizing the absolute continuity of the convolution of orbital measures in a classical Lie algebra, Can. J. Math. 68(2016), 841–874.
• K. Hare, D. Johnstone, F. Shi and W-K. Yeung, L2-singular dichotomy for exceptional Lie groups and algebras, J. Aust. Math. Soc. 95(2013), 362–382.
• S. Gupta and K. Hare, Smoothness of convolutions of zonal measures on compact, symmetric spaces, J. Math. Anal. Appl. 402 (2013), 668–678.
• K. Hare and P. Skoufranis, The smoothness of orbital measures on exceptional Lie groups and algebras, J. Lie Theory 21 (2011), 987–1007.
• S. Gupta and K. Hare, L2 - singular dichotomy for orbital measures on complex groups, Boll. Un. Math. Ital. (9) 3 (2010), 409–419.
• S. Gupta and K. Hare, Smoothness of convolution powers of orbital measures on the symmetric spaces SU(n)/SO(n), Monat. Math. 159 (2010), 27–43.
• S. Gupta and K. Hare, L2 - singular dichotomy for orbital measures of classical compact Lie groups, Adv. Math. 222 (2009), 1521–1573.
• S. Gupta and K. Hare, Convolutions of generic orbital measures in compact symmetric spaces, Bull. Aust. Math. Soc. 79 (2009), 513–522.
• S. Gupta, K. Hare and S. Seyfaddini, L2 - singular dichotomy for orbital measures of classical simple Lie algebras, Math. Zeit. 262 (2009), 91–124.
• S. Gupta and K. Hare, Dichotomy problem for orbital measures of SU(n), Monatsch. Math., 146 (2005), 227–238.
• K. Hare and K. Yeats, Size of characters of exceptional Lie groups, J. Aust. Math. Soc., 77 (2004), 1–16.
• D. Grow and K. Hare, Independence of characters on non-abelian groups, Proc. Amer. Math. Soc., 132 (2004), 3641–3651.
• K. Hare and W-L. Yee, The singularity of orbital measures on compact Lie groups, Rev. Iberoamericana, 20 (2004), 517–530.
• S. Gupta and K. Hare, Singularity of orbits in classical Lie algebras, Geometric and Functional Analysis, 13 (2003), 815–844.
• S. Gupta and K. Hare, Singularity of orbits in SU(n), Israel J., 130 (2002), 93–107.
• K. Hare, D. Wilson and W-L. Yee, Pointwise estimates of the size of characters of compact Lie groups, J. Aust. Math. Soc., 69 (2000), 61–84.
• K. Hare, The size of characters of compact Lie groups, Studia Math. 129 (1998), 1–18.

(b) Fractals and harmonic analysis

• K. Hare and I. Garcia, Properties of quasi-Assouad, accepted by Ann. Acad. Sci. Fenn. Math.
• K. Hare, I. Garcia and F. Mendivil, Intermediate Assouad-like dimensions, accepted by J. Fractal Geometry.
• K. Hare, I. Garcia and F. Mendivil, Almost sure Assouad-like dimensions of complementary sets, accepted by Math. Zeitscrift.
• K. Hare, K. G. Hare and W. Shen, The Lq spectrum for a class of self-similar measures with overlap, accepted by Asian J. Math.
• K. Hare, K. G. Hare and A. Rutar, When the WSC implies the generalized FT condition, accepted by Proc. Amer. Math. Soc.
• K. Hare and K. G. Hare, Intermediate Assouad-like dimensions for measures, accepted by Fractals.
• K. Hare, C. Cabrelli and U. Molter, Riesz bases of exponentials and the Bohr topology, accepted by Proc. Amer. Math. Soc.
• K. Hare and S. Troscheit, Lower Assouad dimension and regularity, accepted by Proc. Camb. Phil. Soc.
• K. Hare, F. Mendivil and L. Zuberman, Measures with specified support and arbitrary Assouad dimension, Proc. Amer. Math. Soc. 184(2020), 3881–3895.
• K. Hare, K. G. Hare and S. Troscheit, Quasi-doubling self-similar measures with overlaps, J Fractal Geometry, 7(2020), 233–270.
• K. Hare, K. G. Hare, B. Morris and W. Shen, Entropy of Cantor-like measures, Acta. Math. Hung. 159(2019), 563–588.
• K. Hare and K. G. Hare, Local dimensions of overlapping self-similar measures, Real Analysis Exch. 44(2019), 247–266.
• K. Hare, J. Fraser, K. G. Hare, S. Troscheit and H. Yu, The Assouad spectrum and the quasi-Assouad dimension: a tale of two spectra, Ann. Acad. Fenn. 44(2019), 379–387.
• K. Hare, K. G. Hare and K. Matthews, Local dimensions of measures of finite type on the torus, Asian. J. Math. 23(2019), 127–155.
• K. Hare, K. G. Hare and S. Troscheit, Local dimensions of random honogeneous self-similar measures: strong separation and finite type, Math. Nach., 291(2018), 2397–2426.
• K. Hare, K. G. Hare and M. Ng, Local dimensions of measures of finite type II - measures without full support and with non-regular probabilities, Can. J. MAth. 70(2018), 824–867.
• K. Hare, I. Garcia and F. Mendivil, Assouad dimensions of complementary sets, Proc. Royal Soc. Edinburgh, 148A(2018), 517–540.
• K. Hare, K. G. Hare and G. Simms, Local dimensions of measures of finite type III - measures that are not equicontractive, J. Math. Anal. and Appl. 458(2018), 1653–1677. Corr. J. Math. Anal. and Appl. 483(2020), 123550.
• K. Hare, K. G. Hare and K. Matthews, Local dimensions of measures of finite type, J. Fractal Geometry, 2(2016), 331–376.
• K. Hare, Self-affine measures that are Lp-improving, Colloq. Math. 139(2015), 299–243.
• K. Hare, F. Mendivil and L. Zuberman, Packing and Hausdorff measures of Cantor sets associated with series, Real Anal. Exch. 40(2015), 421–433.
• K. Hare and M. Ng, Hausdorff and packing measure of balanced Cantor sets, Real Anal. Exch. 40(2014), 113–128.
• C. Bruggeman, C. Mak and K. Hare, Multifractal spectrum of self-similar measures with overlap, Nonlinearity 27 (2014), 227–256.
• C. Bruggeman and K. Hare, Multi-fractal analysis of convolution powers of measures, Real Anal. Exch. 38 (2012/13), 391–408.
• K. Hare, F. Mendevil and L. Zuberman, The sizes of rearrangements of Cantor sets, Can. Math. Bull. 56 (2013), 354–365.
• K. Hare, B. Steinhurst, A. Teplyaev and D. Zhou, Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals, Math. Res. Lett. 19 (2012), 537–553.
• P-W. Fong, K. Hare and D. Johnstone, Multifractal analysis for convolutions of overlapping Cantor measures, Asian J. Math. 15 (2011), 53–69.
• K. Hare and L. Zuberman, Classifying Cantor sets by their multifractal spectrum, Non-Linearity, 23 (2010), 2919–2933.
• C. Cabrelli, K. Hare and U. Molter, Classifying Cantor sets by their fractal dimensions, Proc. Amer. Math. Soc., 138 (2010), 3965–3974.
• K. Hare and D. Zhou, Gaps in the ratios of the spectrum of Laplacians on fractals, Fractals 17 (2009), 523–535.
• K. Hare, P. Mohanty and M. Roginskaya, General energy formula, Math. Scand., 101 (2007), 29–47.
• M. Allen, G. Cruttwell, J.-O. Ronning and K. Hare, Dimensions of fractals in the large, Chaos, Solitons and Fractals, 31 (2007), 5–13.
• K. Hare and M. Roginskaya, Lp-Improving properties of measures of positive energy dimension, Colloq. Math., 102 (2005), 73–86.
• K. Hare and M. Roginskaya, Energy of signed measures, Proc. Amer. Math. Soc., 132 (2004), 397–406.
• K. Hare and J-O. Ronning, Fractal dimensions of infinite product spaces, Int. J. Pure & App. Math., 14 (2004), 136–169.
• K. Hare and M. Roginskaya, Multipliers of spherical harmonics and energy of measures on the sphere, Arkiv. Mat., 41 (2003), 281–294.
• K. Hare and M. Roginskaya, A Fourier series formula for energy of measures with applications to Riesz products, Proc. Amer. Math. Soc., 131 (2003), 165–174.
• K. Hare and M. Roginskaya, Energy of measures on compact Riemannian manifolds, Studia Math., 159 (2003), 291–314.
• C. Cabrelli, K. Hare and U. Molter, Sums of Cantor sets yielding an interval, J. Aust. Math. Soc., 73 (2002) 405–418.
• K. Hare and S. Yazdani, Quasi self-similarity and multifractal analysis of Cantor measures, Real Analysis Exch., 27 (2001/2), 287–307.
• K. Hare and T. O’Neil, N-Fold Sums of Cantor sets, Mathematika, 47 (2000) 243–250.
• C. Cabrelli, K. Hare and U. Molter, Sums of Cantor sets, Ergodic Theory and Dynamical systems 17 (1997), 1299–1313.

(c) Thin Sets

• K. Hare and P. Mohanty, A non-abelian, non-Sidon completely bounded Lambda(p) set, accepted by Can. Math. Bull.
• K. Hare and R. Yang, Sidon sets are proportionally Sidon with small Sidon constants, Can. Math. Bull. 62(2019), 798–809.
• K. Hare and T. Ramsey, The ubiquity of Sidon sets that are not I0, Acta. Sci. Math. (Szeged) 82(2016), 509–518.
• K. Hare and P. Mohanty, Completely bounded Lambda(p) sets that are not Sidon, Proc. Amer. Math. Soc., 144(2016), 2861–2869.
• K. Hare and T. Ramsey, The relationship between e-Kronecker sets and Sidon sets, Can. Bull. Math. 59(2016), 521–527.
• K. Hare and T. Ramsey, Exact Kronecker constants of three element sets, Acta Math. Hung. 146(2015), 306–331.
• K. Hare and T. Ramsey, Kronecker constants of arithmetic progressions, Experimental Math. 23 (2014), 414–422.
• K. Hare and S. Yamagishi, A generalization of Erd ̋os-Renyi to m-fold sums and differences, Acta Arith. 166 (2014), 55–67.
• K. Hare and T. Ramsey, Exact Kronecker constants of Hadamard sets, Colloq. Math. 130 (2013), 39–49.
• C. Graham and K. Hare, Existence of large ε-Kronecker sets and FFI0(U) sets in discrete abelian groups, Colloq. Math. 127 (2012), 1–15.
• K. Hare and T. Ramsey, Kronecker constants for finite subsets of integers, J. Fourier Anal. and Applications 18 (2012), 326–366.
• C. Graham and K. Hare, Characterizations of some classes of I0 sets, Rocky Mtn. J. 40 (2010), 513–525.
• C. Graham and K. Hare, Sets of zero discrete harmonic density, Math. Proc. Camb. Phil. Soc. 148 (2010), 253–266.
• D. Grow and K. Hare, Central interpolation sets for compact groups and hypergroups, Glasgow Math. J. 51 (2009), 593–603.
• C. Graham, K. Hare and T. Ramsey, Union problems for I0 sets, Acta Sci. Math. (Szeged) 75 (2009), 175–195. Corrigendum, Acta Sci. Math. (Szeged) 76 (2010), 487–488.
• C. Graham and K. Hare, I0 sets for compact, connected groups: Interpolation with measures that are non-negative or of small support, J. Aust. Math. Soc. 84 (2008), 199–215.
• C. Graham and K. Hare, Characterizing Sidon sets by interpolation properties of subsets, Colloq. Math. 112 (2008), 175–199.
• C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups IV: Interpolation of non- negative measures, Studia Math., 177 (2006), 9–24.
• C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups I: Arithmetic properties of ε-Kronecker sets, Math. Proc. Camb. Phil. Soc., 140 (2006), 475–489.
• C. Graham, K. Hare and T. Korner, ε-Kronecker sets and I0 sets in abelian groups II: Sparseness of products of ε-Kronecker sets, Math. Proc. Camb. Phil. Soc., 140 (2006), 491–508.
• C. Graham and K. Hare, ε-Kronecker and I0 sets in abelian groups III: Interpolation of measures on small sets, Studia Math., 171 (2005), 15–32.
• K. Hare and T. Ramsey, I0 sets in non-abelian groups, Math. Proc. Comb. Phil. Soc., 135 (2003), 81–98.
• K. Hare, Random weighted Sidon sets, Colloq. Math., 86 (2000), 103–109.
• K. Hare, Sidonicity in compact, abelian hypergroups, Colloq. Math. 96 (1998), 171–180.
• K. Hare and D. Wilson, Weighted p-Sidon sets, J. Aust. Math. Soc. 61 (1996), 73–95.
• K. Hare, Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547–564.
• K. Hare, The support of a function with thin spectrum, Colloq. Math. 67 (1994), 147–154.
• K. Hare and D. Wilson, Structural criterion for the existence of infinite central ∧(p) sets, Trans. Amer. Math. Soc. 337 (1993), 907–925.
• K. Hare, Union results for thin sets, Glasgow Math. Journal 32 (1990), 241–254.
• K. Hare, Strict-2-associatedness for thin sets, Colloq. Math. 56 (1988), 367–381.
• K. Hare, Arithmetic properties of thin sets, Pac. J. Math. 131 (1988), 143–155.
• K. Hare, An elementary proof of a result on ∧(p) sets, Proc. Amer. Math. Soc. 104 (1988), 829–834.

(d) Multipliers and Maximal Operators

• A. Dooley, K. Hare and M. Roginskaya, On Lp-improving measures, Rev. Iberoamericana, 32(2016), 1211–1226.
• K. Hare and M. Roginskaya, Directional maximal operators with smooth densities, Math. Nachr. 282 (2009), 1740–1752.
• K. Hare and P. Mohanty, Distinctness of spaces of Lorentz-Zygmund multipliers, Studia Math., 169 (2005), 143-161.
• K. Hare and F. Ricci, Maximal functions with polynomial densitites in lacunary directions, Trans. Amer. Math. Soc., 355 (2003), 1135–1144.
• K. Hare and J-O. Ronning, Size of Max(p) sets and density bases, J. Fourier Anal. and Appl., 8 (2002), 259–268.
• K. Hare and E. Sato, Spaces of Lorentz multipliers, Can. J. Math, 53 (2001), 565–591.
• K. Hare, Maximal operators and Cantor sets, Can. Math. Bull., 43 (2000), 330–342.
• K. Hare and J.-O. R ̈onning, Applications of generalized Perron trees to maximal functions and density bases, J. Fourier Anal. and App. 4 (1998), 215–227.
• K. Hare, A general approach to Littlewood-Paley theorems for orthogonal families, Can. Math. Bull. 40 (1997), 296–308.
• K. Hare and I. Klemes, On permutations of lacunary intervals, Trans. Amer. Math. Soc. 347 (1995), 4105–4127. (Featured Review in AMS Reviews 95m: 42027)
• K. Hare and R. Grinnell, Lorentz-improving measures, Illinois J. Math. 38 (1994), 366–389.
• K. Hare, Tame Lp-Multipliers, Colloq. Math. 64 (1993), 303–314.
• K. Hare and I. Klemes, A new type of Littlewood-Paley partition, Arkiv for Mat. 30 (1992), 297–307.
• K. Hare, The Size of (L2,Lp) multipliers, Colloq. Math. 63 (1992), 249–262.
• K. Hare, Norm one multipliers, Can. Math. Bull. 35 (1992), 194–203.
• K. Hare, Lp-Improving measures on compact non-abelian groups, J. Aust. Math. Soc. 46 (1989), 402–414.
• C. Graham, K. Hare and D. Ritter, The size of Lp-improving measures, J. Func. Anal. 84 (1989) 472–495.
• K. Hare and I. Klemes, Properties of Littlewood-Paley sets, Math. Proc. Camb. Phil. Soc. 105 (1989), 485–494.
• K. Hare, Properties and examples of (Lp,Lq) multipliers, Indiana Univ. Math. Journal 38 (1989), 211–227.
• K. Hare, A characterization of Lp-improving measures, Proc. Amer. Math. Soc. 102 (1988), 295–299.

(e) Miscellaneous Topics

• S. Gupta and K. Hare, On convolution squares of singular measures, Colloq. Math., 100 (2004), 9–16.
• K. Hare and A. Stokolos, On weak type inequalities for rare maximal functions, Colloq. Math., 83 (2000), 173–182.
• K. Hare and J. Ward, Finite dimensional H-invariant spaces, Bull. Aust. Math. Soc. 56 (1997), 353–361.
• K. Hare and M. Shirvani, The semisimplicity problem for p-adic group algebras, Proc. Amer. Math. Soc. 108 (1990), 653–664.

In refereed conference proceedings

• K. Hare, Multifractal analysis of Cantor-like measures, New trends in applied harmonic analysis - sparse representations, compressed sensing and multifractal analysis. Ed. A. Aldroubi, C. Cabrelli, S. Jaffard and U. Molter, Birkhauser series of Applied and computational harmonic analysis, 350(2015), 1–19.
• K. Hare and A. Stokolos, On the rate of tangential convergence of functions from Hardy spaces, 0 < p < 1, Contemporary Math. 370 (2005), 119–132.
• K. Hare and N. Tomczak-Jaegerman, Banach space properties of translation invariant subspaces of Lp, Analysis at Urbana 1, London Math. Soc. Lecture Note Series 137, ed. E. Berkson, N. Peck & J. Uhl, Cambridge Univ. Press 1989, 185–195. 

Postdoctoral supervision

• Sascha Troscheit, May 2017–Dec. 2018 (co-supervised with K.G. Hare)
• Ignacio Garcia, Aug. 2015–Dec. 2016
• Michael (Ka-Shing) Ng, January–April 2015
• Leandro Zuberman, May 2009–April 2010
• Denglin Zhou, January 2008–August 2009
• Parasar Mohanty, September 2003–August 2004
• Maria Roginskaya, September 2002–August 2003
• Jan-Olav R ̈onning, September 1995–December 1995 and March 1996–June 1996

Graduate Supervision

PhD

• Robert (Xu) Yang, “Sidon and Kronecker-like sets in compact abelian groups”, 2014–2019 (graduated)
• Michael (Ka-Shing) Ng, “Some aspects of Cantor sets”, 2009–2014 (graduated)
• Denglin Zhou, “Spectral analysis of Laplacians on certain fractals”, 2003–2007 (graduated)

MMath

• Claudia Guerro, “Some applications of renewal theorem in fractal geometry”, 2019–2020 (graduated)
• Samuel Desrochers, “Assouad dimension and non-embeddability”, 2019–2020 (graduated)
• Robert (Xu) Yang, “Interpolation sets for compact Abelian groups”, 2013–2014 (graduated)
• David Farahany, “Multiplier problem for the Ball and the Kakeya maximal operator”, 2012–2013 (graduated)
• Sheena Tan, “Hadamard, ε-Kronecker and I0 sets in T”, 2010–2011 (graduated)
• Vincent Chan, “On convolution squares of singular measures”, 2009–2010 (graduated)
• Sheldon Stewart, “Construction of a Besicovitch Set”, 2008–2009 (graduated)
• Pei Pei, “Hausdorff dimension of the random Cantor set”, 2008–2010 (graduated)
• Keon Choi, “Maximal operators in R2”, 2005–2007 (graduated)
• Karen Meagher, “Convolution estimates with Orlicz spaces”, 1995–1997 (graduated)
• Hui Kong, “Riesz Product Measures”, 1991–1992 (graduated)