Michael Ruzhansky

0000-0001-8633-5570
http://ruzhansky.org
Publications398
h-index33
Citations4,220
Highly Influential Citations168
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Quantization on Nilpotent Lie Groups
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
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
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
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
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
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
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
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
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
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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