Richard S Laugesen

1993 …2019
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Research Output 1993 2019

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2019

Pólya’s conjecture fails for the fractional Laplacian

Kwaśnicki, M., Laugesen, R. S. & Siudeja, B. A., Jan 1 2019, In : Journal of Spectral Theory. 9, 1, p. 127-135 9 p.

Research output: Contribution to journalArticle

Fractional Laplacian
eigenvalues
First Eigenvalue
Fractional
analogs
2018

Optimal stretching for lattice points and eigenvalues

Laugesen, R. S. & Liu, S., Jan 1 2018, In : Arkiv for Matematik. 56, 1, p. 111-145 35 p.

Research output: Contribution to journalArticle

Lattice Points
Quadrant
Eigenvalue
Infinity
Radius
2017

Math PhD careers: New opportunities emerging amidst crisis

Baryshnikov, Y., DeVille, L. X. & Laugesen, R. S., Mar 1 2017, In : Notices of the American Mathematical Society. 64, 3, p. 260-264 5 p.

Research output: Contribution to journalArticle

Shortage
Industry
Range of data
Model
Crisis

Optimal stretching for lattice points under convex curves

Ariturk, S. & Laugesen, R. S., Jan 1 2017, In : Portugaliae Mathematica. 74, 2, p. 91-114 24 p.

Research output: Contribution to journalArticle

Convex Curve
Lattice Points
Stretch Factor
Count
Quadrant
2016

Multivariable feedback particle filter

Yang, T., Laugesen, R. S., Mehta, P. G. & Meyn, S. P., Sep 1 2016, In : Automatica. 71, p. 10-23 14 p.

Research output: Contribution to journalArticle

Feedback
Nonlinear filtering
Importance sampling
Boundary value problems
Experiments

Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains

Girouard, A., Laugesen, R. S. & Siudeja, B. A., Feb 1 2016, In : Archive for Rational Mechanics and Analysis. 219, 2, p. 903-936 34 p.

Research output: Contribution to journalArticle

Quasiconformal Maps
Eigenvalue
Upper bound
Roundness
Quasiconformal Mapping
2015

Magnetic spectral bounds on starlike plane domains

Laugesen, R. S. & Siudeja, B. A., Jul 1 2015, In : ESAIM - Control, Optimisation and Calculus of Variations. 21, 3, p. 670-689 20 p.

Research output: Contribution to journalArticle

Spectral Bound
Electron energy levels
Boundary conditions
Magnetic fields
Fluxes

Poisson's equation in nonlinear filtering

Laugesen, R. S., Mehta, P. G., Meyn, S. P. & Raginsky, M., Jan 1 2015, In : SIAM Journal on Control and Optimization. 53, 1, p. 501-525 25 p.

Research output: Contribution to journalArticle

Nonlinear filtering
Nonlinear Filtering
Nonlinear Filters
Poisson equation
Poisson's equation
2014

Sharp spectral bounds on starlike domains

Laugesen, R. S. & Siudeja, B. A., Jan 1 2014, In : Journal of Spectral Theory. 4, 2, p. 309-347 39 p.

Research output: Contribution to journalArticle

Spectral Bound
Sharp Bound
eigenvalues
Roundness
Eigenvalue
2013

Explicit interpolation bounds between hardy space and L 2

Bui, H. Q. & Laugesen, R. S., Oct 1 2013, In : Journal of the Australian Mathematical Society. 95, 2, p. 158-168 11 p.

Research output: Contribution to journalArticle

Bounded Mean Oscillation
Hardy Space
Interpolate
Bounded Linear Operator
Complex Interpolation

Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces

Bui, H. Q. & Laugesen, R. S., Mar 18 2013, In : Journal of Fourier Analysis and Applications. 19, 2, p. 376-409 34 p.

Research output: Contribution to journalArticle

Wavelet Frames
Lebesgue Space
Hardy Space
Wavelets
Frequency Domain
2012

Neumann eigenvalue sums on triangles are (Mostly) minimal for equilaterals

Laugesen, R. S., Pan, Z. C. & Son, S. S., Jan 1 2012, In : Mathematical Inequalities and Applications. 15, 2, p. 381-394 14 p.

Research output: Contribution to journalArticle

Equilateral triangle
Triangle
Eigenvalue
Acute triangle
Isosceles triangle

Sums of Magnetic Eigenvalues are Maximal on Rotationally Symmetric Domains

Laugesen, R. S., Liang, J. & Roy, A., May 1 2012, In : Annales Henri Poincare. 13, 4, p. 731-750 20 p.

Research output: Contribution to journalArticle

eigenvalues
Maximise
Eigenvalue
triangles
boundary conditions

Uniqueness for the continuous wavelet transform

Bui, H-Q. & Laugesen, R. S., 2012, In : Far East J. Appl. Math.. 65, 1, p. 1-11 11 p.

Research output: Contribution to journalArticle

2011

Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Laugesen, R. S. & Siudeja, B. A., Dec 2011, In : Communications in Analysis and Geometry. 19, 5, p. 855-885 31 p.

Research output: Contribution to journalArticle

Dirichlet Eigenvalues
Equilateral triangle
Triangle
Eigenvalue
Dirichlet Laplacian

Frequency-Scale Frames and the Solution of the Mexican Hat Problem

Bui, H. Q. & Laugesen, R. S., Apr 1 2011, In : Constructive Approximation. 33, 2, p. 163-189 27 p.

Research output: Contribution to journalArticle

Mathematical operators
Completeness
Wavelets
Modulation
Synthesis

Moment inequalities for equilibrium measures in the plane

Baernstein, A., Laugesen, R. S. & Pritske, I. E., Jan 1 2011, In : Pure and Applied Mathematics Quarterly. 7, 1, p. 51-86 36 p.

Research output: Contribution to journalArticle

Moment Inequalities
Equilibrium Measure
Centroid
Electrostatics
Moment

Rebuttal of Donnelly's paper on the spectral gap

Ashbaugh, M. S., Henrot, A. & Laugesen, R. S., Oct 1 2011, In : Mathematische Zeitschrift. 269, 1-2, p. 5-7 3 p.

Research output: Contribution to journalArticle

Spectral Gap

Sums of Laplace eigenvalues: Rotations and tight frames in higher dimensions

Laugesen, R. S. & Siudeja, B. A., Sep 23 2011, In : Journal of Mathematical Physics. 52, 9, 093703.

Research output: Contribution to journalArticle

Tight Frame
Laplace
Higher Dimensions
eigenvalues
moments of inertia

Sums of Laplace eigenvalues-rotationally symmetric maximizers in the plane

Laugesen, R. S. & Siudeja, B. A., Mar 15 2011, In : Journal of Functional Analysis. 260, 6, p. 1795-1823 29 p.

Research output: Contribution to journalArticle

Laplace
Eigenvalue
Equilateral triangle
Tight Frame
Parallelogram

Wavelets in Littlewood-Paley space, and Mexican hat completeness

Bui, H. Q. & Laugesen, R. S., Mar 1 2011, In : Applied and Computational Harmonic Analysis. 30, 2, p. 204-213 10 p.

Research output: Contribution to journalArticle

Weighted Spaces
Hardy Space
Completeness
Wavelets
Imbedding
2010

Approximately dual frames in Hilbert spaces and applications to Gabor frames

Christensen, O. & Laugesen, R. S., 2010, In : Sampling Theory in Signal and Image Processing. 9, 1-3, p. 77-89 13 p.

Research output: Contribution to journalArticle

Juglans
Dual Frame
Gabor Frames
Hilbert spaces
Hilbert space

Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality

Laugesen, R. S. & Siudeja, B. A., Jul 1 2010, In : Journal of Differential Equations. 249, 1, p. 118-135 18 p.

Research output: Contribution to journalArticle

Isosceles triangle
Triangle
Acute triangle
Eigenvalue
Symmetry
2009

A computable fourier condition generating alias-free sampling lattices

Lu, Y. M., Do, M. N. & Laugesen, R. S., Jan 1 2009, In : IEEE Transactions on Signal Processing. 57, 5, p. 1768-1782 15 p.

Research output: Contribution to journalArticle

Sampling
Fourier transforms
Filter banks
Testing
Chemical analysis

Gabor dual spline windows

Laugesen, R. S., Sep 1 2009, In : Applied and Computational Harmonic Analysis. 27, 2, p. 180-194 15 p.

Research output: Contribution to journalArticle

Splines
Knot
Spline
Polynomial Splines
Modulation

Maximizing Neumann fundamental tones of triangles

Laugesen, R. S. & Siudeja, B. A., Dec 24 2009, In : Journal of Mathematical Physics. 50, 11, 112903.

Research output: Contribution to journalArticle

triangles
Triangle
eigenvalues
Eigenvalue
Equilateral triangle
2008

Affine synthesis onto lebesgue and hardy spaces

Bui, H. Q. & Laugesen, R. S., Dec 16 2008, In : Indiana University Mathematics Journal. 57, 5, p. 2203-2233 31 p.

Research output: Contribution to journalArticle

Lebesgue Space
Hardy Space
Mixed Norm Space
Synthesis
Norm

Affine synthesis onto L p when 0 < p≤ 1

Laugesen, R. S., Apr 1 2008, In : Journal of Fourier Analysis and Applications. 14, 2, p. 235-266 32 p.

Research output: Contribution to journalArticle

Synthesis
Decomposition
Atomic Decomposition
P-space
Operator

Approximation and spanning in the hardy space, by affine systems

Bui, H. Q. & Laugesen, R. S., Aug 1 2008, In : Constructive Approximation. 28, 2, p. 149-172 24 p.

Research output: Contribution to journalArticle

Lacunary Sequence
Affine Systems
Compact Support
Hardy Space
Regularity Conditions

Sobolev spaces and approximation by affine spanning systems

Bui, H. Q. & Laugesen, R. S., Jun 1 2008, In : Mathematische Annalen. 341, 2, p. 347-389 43 p.

Research output: Contribution to journalArticle

Sobolev Spaces
Affine Systems
Approximation
Strings
Rate of Approximation
2007

On affine frames with transcendental dilations

Laugesen, R. S., Jan 1 2007, In : Proceedings of the American Mathematical Society. 135, 1, p. 211-216 6 p.

Research output: Contribution to journalArticle

Affine Systems
Transcendental
Cancellation
Dilation
Integer

On convex surfaces with minimal moment of inertia

Freitas, P., Laugesen, R. S. & Liddell, G. F., Jan 1 2007, In : Journal of Mathematical Physics. 48, 12, 122902.

Research output: Contribution to journalArticle

Convex Surface
Moment of inertia
moments of inertia
Triangular prism
Truncated tetrahedron
2005

Affine systems that span lebesgue spaces

Bui, H. Q. & Laugesen, R. S., Oct 1 2005, In : Journal of Fourier Analysis and Applications. 11, 5, p. 533-556 24 p.

Research output: Contribution to journalArticle

Affine Systems
Lebesgue Space
Linear Combination
Partition of Unity
Dilation

Another way to say subsolution: The maximum principle and sums of Green functions

Laugesen, R. S. & Watson, N. A., Jan 1 2005, In : Mathematica Scandinavica. 97, 1, p. 127-153 27 p.

Research output: Contribution to journalArticle

Subsolution
Maximum Principle
Green's function
Zeroth
Converse

New dissipated energies for the thin fluid film equation

Laugesen, R. S., Sep 1 2005, In : Communications on Pure and Applied Analysis. 4, 3, p. 613-634 22 p.

Research output: Contribution to journalArticle

Dissipate
Fluid
Hele-Shaw
Fluids
Conserve
2003

Potential Theory of the Farthest-Point Distance Function

Laugesen, R. S. & Pritsker, I. E., Jan 1 2003, In : Canadian Mathematical Bulletin. 46, 3, p. 373-387 15 p.

Research output: Contribution to journalArticle

Farthest Point
Potential Theory
Distance Function
Compact Set
Logarithmic Potential
2002

A characterization of the higher dimensional groups associated with continuous wavelets

Laugesen, R. S., Weaver, N., Weiss, G. L. & Wilson, E. N., Dec 1 2002, In : Journal of Geometric Analysis. 12, 1, p. 89-102 14 p.

Research output: Contribution to journalArticle

Wavelets
High-dimensional
Subgroup

Energy levels of steady states for thin-film-type equations

Laugesen, R. S. & Pugh, M. C., Jul 1 2002, In : Journal of Differential Equations. 182, 2, p. 377-415 39 p.

Research output: Contribution to journalArticle

Energy Levels
Electron energy levels
Thin Films
Orbits
Thin films
Heteroclinic Orbit
Thin Films
Singularity
Structural Stability
Rupture

Translational averaging for completeness, characterization and oversampling of wavelets

Laugesen, R. S., 2002, In : Collectanea Mathematica. 53, 3, p. 211-249 39 p.

Research output: Contribution to journalArticle

2001

Completeness of Orthonormal Wavelet Systems for Arbitrary Real Dilations

Laugesen, R. S., Nov 1 2001, In : Applied and Computational Harmonic Analysis. 11, 3, p. 455-473 19 p.

Research output: Contribution to journalArticle

Orthonormal
Dilation
Completeness
Wavelets
Oversampling
2000

Binary forms, equiangular polygons and harmonic measure

Bean, M. A. & Laugesen, R. S., Jan 1 2000, In : Rocky Mountain Journal of Mathematics. 30, 1, p. 15-62 48 p.

Research output: Contribution to journalArticle

Equiangular
Binary Forms
Harmonic Measure
Polygon
Unit circle

Eigenvalues of strings and cylinders with variable mass density

Laugesen, R. S., Apr 2000, In : Communications in Analysis and Geometry. 8, 2, p. 393-443 51 p.

Research output: Contribution to journalArticle

Strings
Eigenvalue
Eigenvalues

Linear stability of steady states for thin film and Cahn-Hilliard type equations

Laugesen, R. S. & Pugh, M. C., Jan 1 2000, In : Archive for Rational Mechanics and Analysis. 154, 1, p. 3-51 49 p.

Research output: Contribution to journalArticle

Cahn-Hilliard
Linear Stability
Thin Films
Thin films
Boundary conditions

Properties of steady states for thin film equations

Laugesen, R. S. & Pugh, M. C., Jan 1 2000, In : European Journal of Applied Mathematics. 11, 3, p. 293-351 59 p.

Research output: Contribution to journalArticle

Thin Film Equation
Contact angle
Thin films
Contact Angle
Non-negative
1998

Eigenvalues of Laplacians with mixed boundary conditions, under conformal mapping

Laugesen, R. S., Mar 1998, In : Illinois Journal of Mathematics. 42, 1, p. 19-39 21 p.

Research output: Contribution to journalArticle

Mixed Boundary Conditions
Conformal Mapping
Eigenvalue

Eigenvalues of the Laplacian inhomogeneous membranes

Laugesen, R. S., Apr 1998, In : American Journal of Mathematics. 120, 2, p. 305-344 40 p.

Research output: Contribution to journalArticle

Membrane
Eigenvalue
Nonnegative Curvature
First Eigenvalue
Concentric

Eigenvalues of the Laplacian on inhomogeneous membranes

Laugesen, R. S., 1998, In : American Journal of Mathematics. 120, 2, p. 305-344 40 p.

Research output: Contribution to journalArticle

Extremals for Eigenvalues of Laplacians under Conformal Mapping

Laugesen, R. S. & Morpurgo, C., May 10 1998, In : Journal of Functional Analysis. 155, 1, p. 64-108 45 p.

Research output: Contribution to journalArticle

Conformal Mapping
Dirichlet Boundary Conditions
Eigenvalue
Conformal Map
Laplace-Beltrami Operator
1997

Planar harmonic maps with inner and Blaschke dilatations

Laugesen, R. S., Jan 1 1997, In : Journal of the London Mathematical Society. 56, 1, p. 37-48 12 p.

Research output: Contribution to journalArticle

Planar Maps
Dilatation
Harmonic Maps