Quantization of pseudo-differential operators on the torus
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Publication:620418
DOI10.1007/s00041-009-9117-6zbMath1252.58013arXiv0805.2892OpenAlexW2000063290MaRDI QIDQ620418
Michael Ruzhansky, Ville Turunen
Publication date: 19 January 2011
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.2892
Pseudodifferential operators as generalizations of partial differential operators (35S05) Pseudodifferential and Fourier integral operators on manifolds (58J40) Fourier series and coefficients in several variables (42B05) Fourier integral operators applied to PDEs (35S30)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Weyl's formula in the spectral theory of automorphic functions
- Ellipticity, Fredholmness and spectral invariance of pseudo-differential operators on \({{\mathbb S}^1}\)
- Singular ordinary differential operators and pseudodifferential equations
- Pseudo-differential operators on Besov spaces
- Spline approximation methods for multidimensional periodic pseudodifferential equations
- On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Exponential sums and nonlinear Schrödinger equations
- On symbol analysis of periodic pseudodifferential operators
- Generalization and use of the theory of pseudodifferential operators in the modeling of some problems in mechanics.
- Foundations of time-frequency analysis
- An algebra of pseudodifferential operators
- Commutator characterization of periodic pseudodifferential operators
- Weighted Sobolev L2 estimates for a class of Fourier integral operators
- Noncommutative microlocal analysis. I
- Local and Global Descriptions of Periodic Pseudodifferential Operators
- On the Toroidal Quantization of Periodic Pseudo-Differential Operators
- On the Fourier Analysis of Operators on the Torus
- The fourier series representation of pseudo-differentiai operators on closed curves
- On a theory of pseudo-differential operators on the circle
- Characterizations of pseudodifferential operators on the circle
- Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces
- Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
- Modeling of aerodynamic and wave diffraction problems and extensions of Cauchy type integral operators on closed and open curves
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