Steven Morris Zelditch

  • 2595 Citations
1982 …2021
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Research Output 1982 2019

2019
3 Citations (Scopus)

Central limit theorem for spectral partial bergman kernels

Zelditch, S. M. & Zhou, P., Jan 1 2019, In : Geometry and Topology. 23, 4, p. 1961-2004 44 p.

Research output: Contribution to journalArticle

Bergman Kernel
Central limit theorem
Subspace
Density of States
Partial

Interface asymptotics of Partial Bergman kernels around a critical level

Zelditch, S. & Zhou, P., Jan 1 2019, In : Arkiv for Matematik. 57, 2, p. 471-492 22 p.

Research output: Contribution to journalArticle

Open Access
Bergman Kernel
Partial
Tube
Morse Function
Series
2 Citations (Scopus)

Interface asymptotics of partial bergman kernels on S1-symmetric Kähler manifolds

Zelditch, S. & Zhou, P., Jan 1 2019, In : Journal of Symplectic Geometry. 17, 3, p. 793-856 64 p.

Research output: Contribution to journalArticle

Bergman Kernel
Partial
Equivariant
Invariant Manifolds
Scaling

Mathematics of quantum chaos in 2019

Zelditch, S., Oct 2019, In : Notices of the American Mathematical Society. 66, 9, p. 1412-1422 11 p.

Research output: Contribution to journalArticle

Open Access
Quantum Chaos
2018

Log-scale equidistribution of nodal sets in Grauert tubes

Chang, R. & Zelditch, S. M., Jan 1 2018, (Accepted/In press) In : Journal des Mathematiques Pures et Appliquees.

Research output: Contribution to journalArticle

Equidistribution
Eigenvalues and eigenfunctions
Length Scale
Eigenfunctions
Tube
2 Citations (Scopus)

Log-Scale Equidistribution of Zeros of Quantum Ergodic Eigensections

Chang, R. & Zelditch, S. M., Dec 1 2018, In : Annales Henri Poincare. 19, 12, p. 3783-3814 32 p.

Research output: Contribution to journalArticle

Equidistribution
Polynomial Decay
Decay of Correlations
Unitary Operator
Zero
2 Citations (Scopus)

Pointwise weyl law for partial bergman kernels

Zelditch, S. & Zhou, P., Jan 1 2018, Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. Hitrik, M., Tamarkin, D., Tsygan, B. & Zelditch, S. (eds.). Springer New York LLC, p. 589-634 46 p. (Springer Proceedings in Mathematics and Statistics; vol. 269).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Spectral Projection
Bergman Kernel
Partial
Tauberian theorem
Uniformly continuous

Preface

Hitrik, M., Tamarkin, D., Tsygan, B. & Zelditch, S., Jan 1 2018, In : Springer Proceedings in Mathematics and Statistics. 269, p. v-Xiv

Research output: Contribution to journalEditorial

1 Citation (Scopus)

Quantum Ergodic Sequences and Equilibrium Measures

Zelditch, S., Feb 1 2018, In : Constructive Approximation. 47, 1, p. 89-118 30 p.

Research output: Contribution to journalArticle

Equilibrium Measure
Metric
Orthonormal basis
Levenberg-Marquardt
Line Bundle
2017

Addendum to "Critical values of random analytic functions on complex manifolds"

Feng, R. & Zelditch, S. M., 2017, In : Indiana University Mathematics Journal. 66, p. 23-29 7 p.

Research output: Contribution to journalArticle

Scaling of Harmonic Oscillator Eigenfunctions and Their Nodal Sets Around the Caustic

Hanin, B., Zelditch, S. M. & Zhou, P., Mar 1 2017, In : Communications in Mathematical Physics. 350, 3, p. 1147-1183 37 p.

Research output: Contribution to journalArticle

Caustic
Eigenspace
Harmonic Oscillator
harmonic oscillators
Eigenfunctions
2 Citations (Scopus)

Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary

Sogge, C. D. & Zelditch, S., Aug 3 2017, In : Communications in Partial Differential Equations. 42, 8, p. 1249-1289 41 p.

Research output: Contribution to journalArticle

Eigenvalues and eigenfunctions
Cauchy
Eigenfunctions
Norm
Riemannian Manifold
5 Citations (Scopus)

The Cauchy problem for the homogeneous Monge-Ampère equation, III. Lifespan

Rubinstein, Y. A. & Zelditch, S., Apr 2017, In : Journal fur die Reine und Angewandte Mathematik. 2017, 724

Research output: Contribution to journalArticle

Life Span
Cauchy Problem
Uniqueness of Solutions
Weak Solution
Differentiable
2016

A Note on Lp-norms of Quasi-modes

Sogge, C. D. & Zelditch, S. M., 2016, Some Topics in Harmonic Analysis and Applications. Li, J., Li, X. & Lu, G. (eds.). International Press of Boston, Inc., p. 385-397 13 p. (Advanced Lectures in Mathematics; vol. 34).

Research output: Chapter in Book/Report/Conference proceedingChapter

Ergodicité quantique des fonctions d'Eisenstein

Translated title of the contribution: Quantum ergodicity for Eisenstein functionsBonthonneau, Y. & Zelditch, S. M., Sep 1 2016, In : Comptes Rendus Mathematique. 354, 9, p. 907-911 5 p.

Research output: Contribution to journalArticle

Hyperbolic Surface
Eisenstein Series
Ergodicity
High-dimensional
Curvature
9 Citations (Scopus)

Focal points and sup-norms of eigenfunctions

Sogge, C. D. & Zelditch, S., Jan 1 2016, In : Revista Matematica Iberoamericana. 32, 3, p. 971-994 24 p.

Research output: Contribution to journalArticle

Eigenfunctions
Perron-Frobenius Operator
Norm
Geodesic Flow
Trace Formula
6 Citations (Scopus)

Focal points and sup-norms of eigenfunctions II: The two-dimensional case

Sogge, C. D. & Zelditch, S., Jan 1 2016, In : Revista Matematica Iberoamericana. 32, 3, p. 995-999 5 p.

Research output: Contribution to journalArticle

Eigenfunctions
Norm
Circle Map
Geodesic
Pole

Geodesics and global harmonic analysis

Zelditch, S. M., Jan 1 2016, In : Notices of the American Mathematical Society. 63, 1, p. 15-17 3 p.

Research output: Contribution to journalComment/debate

Global Analysis
Harmonic Analysis
Geodesic
1 Citation (Scopus)

Heat kernel measures on random surfaces

Klevtsov, S. & Zelditch, S., Jan 1 2016, In : Advances in Theoretical and Mathematical Physics. 20, 1, p. 135-164 30 p.

Research output: Contribution to journalArticle

Random Surfaces
Heat Kernel
Metric
heat
infinity
3 Citations (Scopus)

Logarithmic lower bound on the number of nodal domains

Zelditch, S., Jan 1 2016, In : Journal of Spectral Theory. 6, 4, p. 1047-1086 40 p.

Research output: Contribution to journalArticle

Nodal Domain
Eigenfunctions
Logarithmic
eigenvectors
eigenvalues
12 Citations (Scopus)
Nodal Domain
Curved Surface
Singular Point
Isometric
Involution
10 Citations (Scopus)

Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary

Jung, J. & Zelditch, S., Apr 1 2016, In : Mathematische Annalen. 364, 3-4, p. 813-840 28 p.

Research output: Contribution to journalArticle

Nodal Domain
Curved Surface
Eigenfunctions
Eigenvalue
Counting Problems
3 Citations (Scopus)

Off-Diagonal Decay of Toric Bergman Kernels

Zelditch, S. M., Dec 1 2016, In : Letters in Mathematical Physics. 106, 12, p. 1849-1864 16 p.

Research output: Contribution to journalArticle

Bergman Kernel
Orbit
Decay
orbits
Metric
3 Citations (Scopus)

Szegő kernels and Poincaré series

Lu, Z. & Zelditch, S., Nov 1 2016, In : Journal d'Analyse Mathematique. 130, 1, p. 167-184 18 p.

Research output: Contribution to journalArticle

Projector
kernel
Series
Universal Cover
Surjectivity
2015
3 Citations (Scopus)

Equidistribution of phase shifts in semiclassical potential scattering

Gell-Redman, J., Hassell, A. & Zelditch, S. M., Apr 17 2015, In : Journal of the London Mathematical Society. 91, 1, p. 159-179 21 p.

Research output: Contribution to journalArticle

Equidistribution
Unit circle
Phase Shift
Scattering
Eigenvalue

Gaussian beams on Zoll manifolds and maximally degenerate Laplacians

Zelditch, S. M., 2015, Spectral Theory and Partial Differential Equations. Friedlander, L. & Garnett, J. (eds.). American Mathematical Society, p. 169-197 29 p. (Contemporary Mathematics; vol. 640).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Hausdorff measure of nodal sets of analytic Steklov eigenfunctions

Zelditch, S., Jan 1 2015, In : Mathematical Research Letters. 22, 6, p. 1821-1842 22 p.

Research output: Contribution to journalArticle

Hausdorff Measure
Eigenfunctions
Dirichlet
Riemannian Manifold
Eigenvalue
6 Citations (Scopus)

Nodal sets of random eigenfunctions for the isotropic harmonic oscillator

Hanin, B., Zelditch, S. & Zhou, P., Jan 1 2015, In : International Mathematics Research Notices. 2015, 13, p. 4813-4839 27 p.

Research output: Contribution to journalArticle

Harmonic Oscillator
Eigenfunctions
Hypersurface
Ball
Eigenvalue

Scaling asymptotics of heat kernels of line bundles

Ma, X., Marinescu, G. & Zelditch, S. M., 2015, nalysis, Complex Geometry, and Mathematical Physics: In Honor of Duong H. Phong. Fehan, P. M. N., Song, J., Weinkove, B. & Wentworth, R. A. (eds.). American Mathematical Society, p. 175-202 28 p. (Contemporary Mathematics; vol. 644).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2014
5 Citations (Scopus)

Completeness of boundary traces of eigenfunctions

Han, X., Hassell, A., Hezari, H. & Zelditch, S. M., Jan 1 2014, In : Proceedings of the London Mathematical Society. 111, 3, p. 749-773 25 p.

Research output: Contribution to journalArticle

Eigenfunctions
Completeness
Trace
Billiards
Neumann Boundary Conditions
6 Citations (Scopus)

Critical values of random analytic functions on complex manifolds

Feng, R. & Zelditch, S., Jan 1 2014, In : Indiana University Mathematics Journal. 63, 3, p. 651-686 36 p.

Research output: Contribution to journalArticle

Random Function
Complex Manifolds
Critical value
Analytic function
Ensemble
4 Citations (Scopus)

Ergodicity and intersections of nodal sets and geodesics on real analytic surfaces

Zelditch, S. M., Feb 1 2014, In : Journal of Differential Geometry. 96, 2, p. 303-351 49 p.

Research output: Contribution to journalArticle

Ergodicity
Geodesic
Intersection
Complexification
Geodesic Flow

Matrix elements of Fourier Integral Operators

Zelditch, S. M., 2014, Inverse Problems and Applications. Stefanov, P., Vasy, A. & Zworski, M. (eds.). American Mathematical Society, p. 281-309 29 p. (Contemporary Mathematics; vol. 615).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Median and mean of the supremum of L2 normalized random holomorphic fields

Feng, R. & Zelditch, S. M., Apr 15 2014, In : Journal of Functional Analysis. 266, 8, p. 5085-5107 23 p.

Research output: Contribution to journalArticle

Supremum
Concentration of Measure
Bergman Kernel
Entropy Method
Covering number
11 Citations (Scopus)

On eigenfunction restriction estimates and L4-bounds for compact surfaces with nonpositive curvature

Sogge, C. D. & Zelditch, S. M., Jan 5 2014, Advances in Analysis: The Legacy of Elias M. Stein. Princeton University Press, Vol. 9781400848935. p. 447-462 16 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

Nonpositive Curvature
Eigenfunctions
Restriction
Estimate
7 Citations (Scopus)
Orthonormal basis
Hilbert spaces
Ergodicity
Higher Dimensions
Laplace transformation
3 Citations (Scopus)

Stability and integration over Bergman metrics

Klevtsov, S. & Zelditch, S. M., Jan 1 2014, In : Journal of High Energy Physics. 2014, 7, 100.

Research output: Contribution to journalArticle

partitions
functionals
rays
energy

Survey on the Inverse Spectral Problem

Zelditch, S. M., 2014, In : Notices of the International Congress of Chinese Mathematicians. 2, 2, p. 1-20 20 p.

Research output: Contribution to journalArticle

2013

Concerning the L4 norms of typical eigenfunctions on compact surfaces

Sogge, C. D. & Zelditch, S. M., 2013, Recent Developments in Geometry and Analysis. Dong, Y., Fu, J., Lu, G., Sheng, W. & Zhu, X. (eds.). International Press of Boston, Inc., p. 407-423 17 p. (Advanced Lectures in Mathematics; vol. 23).

Research output: Chapter in Book/Report/Conference proceedingChapter

Eigenfunctions and Nodal sets

Zelditch, S. M., 2013, Surveys in Differential Geometry, 2013: Geometry and Topology. Cao, H-D. & Yau, S-T. (eds.). International Press of Boston, Inc., p. 237-308 72 p. (Surveys in Differential Geometry; vol. 18).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Large deviations of empirical measures of zeros on riemann surfaces

Zelditch, S., Feb 11 2013, In : International Mathematics Research Notices. 2013, 3, p. 592-664 73 p.

Research output: Contribution to journalArticle

Empirical Measures
Large Deviation Principle
Line Bundle
Riemann Surface
Large Deviations
14 Citations (Scopus)

Quantum ergodic restriction for cauchy data: Interior que and restricted que

Christianson, H., Toth, J. A. & Zelditch, S., May 1 2013, In : Mathematical Research Letters. 20, 3, p. 465-475 11 p.

Research output: Contribution to journalArticle

Cauchy
Interior
Restriction
Eigenfunctions
Ergodicity
22 Citations (Scopus)

Quantum Ergodic Restriction Theorems: Manifolds Without Boundary

Toth, J. A. & Zelditch, S. M., Apr 1 2013, In : Geometric and Functional Analysis. 23, 2, p. 715-775 61 p.

Research output: Contribution to journalArticle

Geodesic Flow
Fourier Integral Operators
Restriction
Hyperbolic Surface
Closed Geodesics
15 Citations (Scopus)

Random Kähler metrics

Ferrari, F., Klevtsov, S. & Zelditch, S., Apr 1 2013, In : Nuclear Physics B. 869, 1, p. 89-110 22 p.

Research output: Contribution to journalArticle

deviation
approximation
2 Citations (Scopus)

Random Riesz energies on compact Kähler manifolds

Feng, R. & Zelditch, S. M., Jul 24 2013, In : Transactions of the American Mathematical Society. 365, 10, p. 5579-5604 26 p.

Research output: Contribution to journalArticle

Random Polynomials
Zero set
Line Bundle
Compact Manifold
Codimension
2012
11 Citations (Scopus)

C spectral rigidity of the ellipse

Hezari, H. & Zelditch, S. M., Dec 1 2012, In : Analysis and PDE. 5, 5, p. 1105-1132 28 p.

Research output: Contribution to journalArticle

Ellipse
Rigidity
Symmetry
16 Citations (Scopus)

Gravitational actions in two dimensions and the Mabuchi functional

Ferrari, F., Klevtsov, S. & Zelditch, S. M., Jun 21 2012, In : Nuclear Physics B. 859, 3, p. 341-369 29 p.

Research output: Contribution to journalArticle

gravitation
scalars
expansion
geometry
energy
1 Citation (Scopus)

Intertwining the geodesic flow and the Schrödinger group on hyperbolic surfaces

Anantharaman, N. & Zelditch, S. M., Aug 1 2012, In : Mathematische Annalen. 353, 4, p. 1103-1156 54 p.

Research output: Contribution to journalArticle

Hyperbolic Surface
Geodesic Flow
Hilbert space
Wigner Distribution
Quantum Chaos
18 Citations (Scopus)

Lower bounds on the hausdorff measure of nodal sets II

Sogge, H. D. & Zelditch, S., 2012, In : Mathematical Research Letters. 19, 6, p. 1361-1364 4 p.

Research output: Contribution to journalArticle

Hausdorff Measure
Immediately
Lower bound

Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I

Zelditch, S. M., 2012, Spectral Geometry. Barnett, A. H., Gordon, C. S., Perry, P. A. & Uribe, A. (eds.). American Mathematical Society, p. 299-339 41 p. (Proceedings of Symposia in Pure Mathematics; vol. 84).

Research output: Chapter in Book/Report/Conference proceedingConference contribution