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Dr. Julian Edward

Dr. Edward's main area of research is analysis and partial differential equations. He has studied the spectral and inverse spectral properties of Steklov eigenvalues on bounded domains, and the spectral/scattering theory of Schrodinger operators on unbounded Euclidean domains. He has also studied the spectral properties of Jacobi matrices. More recently, he has also studied control and inverse problems.

He has collaborated with political scientist Keith Dougherty on topics in voting theory.

Preprints and publications

(w. S Avdonin) "Controllability for string with attached masses and Riesz bases for asymmetric spaces"

(w. S. Avdonin) "“Boundary control for vibrating string with attached masses”, in submission

(w. S. Hudson and M. Leckband), "Minimal potential results for Neumann Problems", Forum Math.
(w. , Avdonina, N., and Avdonin, S.) " Control and inverse problems for networks of vibrating strings with attached masses", Boundary Inverse problems for networks of strings with attached masses", Proceedings of Dynamical Systems and Applications, 7 (2016), 41-44.

(w. Al-Mulsallam, F, Avdonina, N., and Avdonin, S.) " Control and inverse problems for networks of vibrating strings with attached masses", Nanosystems: Physics, Chemistry, and Mathematics, 2016, 7 (5), 835-841.

(w. Hudson, S. and Leckband, M.) "Existence problems for the p-Laplacian", Forum Math. 27 (2015), no. 2, 1203–1225

(w. Decarli, L., Hudson, S., and Leckband, M.) "Minimal support results for Schrodinger operators", Forum Math. 27 (2015), no. 1, 343–371

(w. K. Dougherty and R. Ragan), The value of formalism: re-examining external costs and decision costs with multiple groups, Public Choice, published online 10.1007/s11127-014-0191-1

( w. Dougherty, K) Voting for Pareto Optimality: a multidimensional analysis. Public Choice, 2012, 151 (3): 655-78.

(w. Dougherty, K) The calculus of consent and constitutional design. Springer, 2011.

(w. Dougherty, K), The properties and Simple versus Absolute Majority Rule: Cases where absences and abstentions matter, Journal of Theoretical Politics, 22 (2010), 85-122.

(w. Dougherty, K), Even or Odd: Assembly Size and Majority Rule,Journal of Politics, 71, (2009) no. 2, pp. 733-747.

Ingham-type inequalities for complex frequencies and applications to control theory, Journal of Mathematical Analysis
and Applications, 324 (2006)

(w. Louis Tebou) Uniform internal controllability for structurally damped beam equation, Asymptotic
Analysis, 47 (2006), 55-83.

(w. Keith Dougherty) A non-equilibrium analysis of Unanimity Rule, Majority Rule, and two Pareto concepts, Economic Inquiry 43, (2005), 855-865.

(w. Keith Dougherty) " The Pareto efficiency and expected cost of k-majority versus rules", Politics, Philosophy, and Economics 3, (2004), 161-189

Trapped modes for periodic structures in waveguides", Math. Methods in Applied Science. 27, (2004), 91-99.

"On the resonances of the Laplacian on waveguides", Journal of Mathematical Analysis and Applications 272, (2002), 89-116.

"Bounds on the number of resonances for certain spaces which are flat at infinity".

"Eigenfunction decay for the Neumann Laplacian on planar domains with horn-like ends", Canadian Mathematical Bulletin, Vol.43 (1), 2000 pp.51-59.
Corrigendum to "Spectral theory for the Neumann Laplacian on planar domains with horn-like ends", Canad. J. Math Vol 52 (1), 2000 pp. 119-122.

"Spectra of Schrodinger operators on planar domains with ends of increasing cross section", Math. Methods Appl. Sci. Vol. 22, pp.139-169, (1999).
"Eigenfunction decay and eigenvalue accumulation for the Laplacian on asymptotically perturbed waveguides", J. London Math. Soc., (2) 59 (1999), 620-636.
with David Pravica "Bounds in resonances of the Laplacian for perturbations of half space", SIAM J. Math. Anal. 30, 1999, 1175-1184.
"Spectrum of the Neumann Laplacian on asymptotic perturbations of the strip"
"Spectrum of the Neumann Laplacian on planar
domains with horn-like ends", Canadian J. Math., {\bf 49}, 1997, 232-262.
``An Inequality for Steklov Eigenvalues for
Planar Domains'', Zeitsdhrift fur angewandte Mathematik
und Physik 45, 1994, pp. 493-496.
``Pre-Compactness of Isospectral Sets of Planar Domains for the Neumann Operator.''}, Communications in Partial Differential Equations, Vol. 18, Numbers 7, 8, 1993, pp. 1249-1270.
``Jacobi Matrices and the Spectrum of the Neumann Operator on a Family of Riemann Surface'', Canadian Journal of Mathematics, Vol. 45, Number 4, 1993, pp. 709-726.
``The Spectra of Jacobi Matrices, Differential Operators
on the Circle, and the su(1,1) Lie Algebra''} SIAM Journal
of Mathematical Analysis, Vol. 24, No. 3, May 1993, pp. 824-831.
``An inverse spectral result for the Neumann Operator on smooth planar domains''}, Journal of Functional Analysis,
Vol. 111, No. 2, February 1993, pp. 312-322.
(with Siye Wu): ``Determinant of the Neumann Operator on smooth Jordan curves,'' AMS Proceedings, Volume 111, Number 2, February 1991, pp 357-363.

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