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Quantization on Nilpotent Lie Groups
- Veronique Fischer, Michael Ruzhansky
- Mathematics
- 22 March 2016
Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5…
Quantization of Pseudo-differential Operators on the Torus
- Michael Ruzhansky, Ville T. Turunen
- Mathematics
- 19 May 2008
AbstractPseudo-differential and Fourier series operators on the torus
${{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}$
are analyzed by using global representations by Fourier series instead of local…
Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
- Michael Ruzhansky, M. Sugimoto
- Mathematics
- 1 January 2006
ABSTRACT The local L 2-mapping property of Fourier integral operators has been established in Hörmander (1971) and in Eskin (1970). In this article, we treat the global L 2-boundedness for a class of…
Global L2-boundedness theorems for a class of Fourier integral operators
- Michael Ruzhansky, M. Sugimoto
- Mathematics
- 13 November 2003
The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of…
The Hardy–Littlewood Maximal Operator
- D. Cruz-Uribe, A. Fiorenza, Michael Ruzhansky, J. Wirth
- Mathematics
- 2014
In this chapter we turn to the study of harmonic analysis on the variable Lebesgue spaces. Our goal is to establish sufficient conditions for the Hardy–Littlewood maximal operator to be bounded on L…
Fourier multipliers on compact Lie groups
- Michael Ruzhansky, J. Wirth
- Mathematics
- 2015
In this paper we prove L p Fourier multiplier theorems for invariant and also noninvariant operators on compactLie groups in the spirit of thewell-knownHörmander–Mikhlin theorem on Rn and its…
An Introduction To Pseudo Differential Operators
- Michael Ruzhansky
- Mathematics
- 2014
an introduction to pseudo differential Li, Keyong and D'Andrea, Raffaello 2006. Trajectory Design of Autonomous Vehicles Based on Motion Primitives and Heuristic Cost-to-Go Functions. p. 3345. an…
Nonharmonic Analysis of Boundary Value Problems
- Michael Ruzhansky, N. Tokmagambetov
- Mathematics
- 3 April 2015
In this paper, we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differential…
$$L^p$$Lp Fourier multipliers on compact Lie groups
- Michael Ruzhansky, J. Wirth
- Mathematics
- 19 February 2011
In this paper we prove $$L^p$$Lp Fourier multiplier theorems for invariant and also non-invariant operators on compact Lie groups in the spirit of the well-known Hörmander–Mikhlin theorem on…
Smoothing properties of evolution equations via canonical transforms and comparison principle
- Michael Ruzhansky, M. Sugimoto
- Mathematics
- 1 August 2012
This paper describes a new approach to global smoothing problems for dispersive and non‐dispersive evolution equations based on the global canonical transforms and the underlying global microlocal…
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