Richard S Laugesen

1993 …2019
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Research Output 1993 2019

2019

BIG career developments for mathematics graduate students

Laugesen, R. S., Levy, R. & Santosa, F., Apr 2019, In : Notices of the American Mathematical Society. 66, 4, p. 523-524 2 p.

Research output: Contribution to journalComment/debate

Open Access

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

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

Shifted lattices and asymptotically optimal ellipses

Laugesen, R. S. & Liu, S., 2018, In : The Journal of Analysis. 26, 1, p. 71-102 32 p.

Research output: Contribution to journalArticle

Asymptotically Optimal
Curve
Quadrant
Lattice Points
Limiting

Spectral theory of partial differential equations

Laugesen, R. S., Jan 1 2018, Contemporary Mathematics. American Mathematical Society, Vol. 720. p. 23-55 33 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Spectral Theory
Partial differential equation
Eigenvalue
Discrete Spectrum
Nonlinear PDE
2017

Math PhD careers: New opportunities emerging amidst crisis

Baryshnikov, Y., DeVille, L. & Laugesen, R., Mar 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

Triangles and other special domains

Laugesen, R. S. & Siudeja, B. O. A., 2017, Shape optimization and spectral theory. De Gruyter Open, Warsaw, p. 149-200 52 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

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

Torsion and ground state maxima: close but not the same

Benson, B. A., Laugesen, R. S., Minion, M. & Siudeja, B. O. A., 2016, In : Bulletin of the Irish Mathematical Society. 78, p. 81-88 8 p.

Research output: Contribution to journalArticle

Nonlinearity
Counterexample
Triangle
Equations
Closeness
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

Poisson's equation in nonlinear filtering

Laugesen, R., Mehta, P. G., Meyn, S. P. & Raginsky, M., Jan 1 2014, In : Proceedings of the IEEE Conference on Decision and Control. 2015-February, February, p. 4185-4190 6 p., 7040041.

Research output: Contribution to journalConference article

Nonlinear filtering
Nonlinear Filtering
Poisson equation
Poisson's equation
Particle Filter

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 L2

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

Tight frames and rotations: sharp bounds on eigenvalues of the Laplacian

Laugesen, R. S., 2013, AMSI International Conference on Harmonic Analysis and Applications. Austral. Nat. Univ., Canberra, Vol. 45. p. 63-82 20 p. (Proc. Centre Math. Appl. Austral. Nat. Univ.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

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

Multivariable feedback particle filter

Yang, T., Laugesen, R. S., Mehta, P. G. & Meyn, S. P., Dec 1 2012, In : Proceedings of the IEEE Conference on Decision and Control. p. 4063-4070 8 p., 6425937.

Research output: Contribution to journalConference article

Particle Filter
Poisson equation
Feedback
Nonlinear filtering
Importance sampling

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

Laugesen, R. S., Pan, Z. C. & Son, S. S., Apr 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 1 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 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., Dec 1 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

A note on constructing affine systems for L 2

Bui, H. Q., Kaiblinger, N. & Laugesen, R. S., Nov 1 2008, In : Applied and Computational Harmonic Analysis. 25, 3, p. 400-406 7 p.

Research output: Contribution to journalLetter

Affine Systems
Norm
Dilation
Expand
Linear Combination

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., Sep 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