6 citations · 15 across the 14 of their papers we have counts for
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estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have -th order contact
Madelyne M. Brown, Melissa Tacy
On a smooth, compact, -dimensional Riemannian manifold, we consider functions that are joint quasimodes of two semiclassical pseudodifferential operators and $…
Filament structure of random waves
Melissa Tacy
We investigate the small scale equidistribution properties of random waves in . Numerical evidence suggests that such objects display a fine scale filament structur…
Small scale equidistribution of random waves generated by an unfair coin flip
Miriam Leonhardt, Melissa Tacy
In this paper we study the small scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is the coefficients take value with…
estimates for joint quasimodes of semiclassical pseudodifferential operators whose characteristic sets have th order contact
Melissa Tacy
In this paper we develop estimates for functions which are joint quasimodes of semiclassical pseudodifferential operators and whose characte…
Stationary phase type estimates for low symbol regularity
Melissa Tacy
The well-known stationary phase formula gives us a way to precisely compute oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter cont…
estimates for joint quasimodes of semiclassical pseudodifferential operators
Melissa Tacy
We develop a set of estimates for functions that are a joint quasimodes (approximate eigenfunctions) of semiclassical pseudodifferential operators $p_{1}(x,hD),\dot…
A note on constructing sharp examples for norms of eigenfunctions and quasimodes near submanifolds
Melissa Tacy
In this note we analyse estimates for Laplacian eigenfunctions and quasimodes and their associated sharp examples. In particular we use previously determined estimates to p…
Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues
Alex Barnett, Andrew Hassell, Melissa Tacy
For smooth bounded domains in , we prove upper and lower bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary dat…
Lp bilinear quasimode estimates
Zihua Guo, Xiaolong Han, Melissa Tacy
In this paper, we investigate the bilinear quasimode estimates on compact Riemannian manifolds. We obtain results in the full range on all -dimensional manifolds w…
Sharp norm estimates of layer potentials and operators at high frequency
Jeffrey Galkowski, Xiaolong Han, Melissa Tacy
In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency . For single layer potentia…
The quantisation of normal velocity does not concentrate on hypersurfaces
Melissa Tacy
We seek to extend work by Christianson-Hassell-Toth \cite{CHT} on restrictions of Neumann data of Laplacian eigenfunctions to interior hypersurfaces to a general semiclassical sett…
Improvement of eigenfunction estimates on manifolds of nonpositive curvature
Andrew Hassell, Melissa Tacy
Let be a compact, boundaryless manifold of dimension with the property that either (i) and has no conjugate points, or (ii) the sectional curvatures of $(…
Semiclassical L^p Estimates of Quasimodes on Curved Hypersurfaces
Andrew Hassell, Melissa Tacy
Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^…
Semiclassical L^p Estimates of Quasimodes on Submanifolds
Melissa Tacy
Let M be a compact manifold and P = P(h) a semiclassical pseudodifferential operator on M . Suppose that u(h) is a L^2 normalised family of functions such that P(h)u(h) is O(h) in…