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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… Expand
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… Expand
Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
- Michael Ruzhansky, Mitsuru 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… Expand
Introduction to pseudo-differential operators
The present notes give introduction to the theory of pseudo-differential operators on Euclidean spaces. The first part is devoted to the necessary analysis of functions, such as basics of the Fourier… Expand
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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… Expand
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- 6
- PDF
Global L2-boundedness theorems for a class of Fourier integral operators
- Michael Ruzhansky, Mitsuru 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… Expand
The optimal filter construction for a general quadratic cost functional
- Michael Ruzhansky, V. Fomin
- Mathematics
- 1996
- 6
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$$L^p$$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… Expand
On multipliers on compact Lie groups
- Michael Ruzhansky, J. Wirth
- Mathematics
- 14 March 2013
In this note we announce Lp multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander-Mikhlin theorem on ℝn and its versions on the… Expand
Hardy, Hardy-Sobolev, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
- Michael Ruzhansky, Nurgissa Yessirkegenov
- Mathematics
- 20 October 2018
In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights for… Expand