Spectral theory of SG pseudo-differential operators on L p ( ℝ ⁿ )

Aparajita Dasgupta; M. W. Wong

Studia Mathematica (2008)

  • Volume: 187, Issue: 2, page 185-197
  • ISSN: 0039-3223

Abstract

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To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on L p ( ℝ ⁿ ) , 1 < p < ∞, and prove that they are equal. The domain of the minimal ( = maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders 0,0 are computed.

How to cite

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Aparajita Dasgupta, and M. W. Wong. "Spectral theory of SG pseudo-differential operators on $L^{p}(ℝⁿ)$." Studia Mathematica 187.2 (2008): 185-197. <http://eudml.org/doc/284819>.

@article{AparajitaDasgupta2008,
abstract = {To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on $L^\{p\}(ℝⁿ)$, 1 < p < ∞, and prove that they are equal. The domain of the minimal ( = maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders 0,0 are computed.},
author = {Aparajita Dasgupta, M. W. Wong},
journal = {Studia Mathematica},
keywords = {pseudo-differential operators; ellipticity; minimal and maximal operators; Fredholm operators; essential spectra; indices},
language = {eng},
number = {2},
pages = {185-197},
title = {Spectral theory of SG pseudo-differential operators on $L^\{p\}(ℝⁿ)$},
url = {http://eudml.org/doc/284819},
volume = {187},
year = {2008},
}

TY - JOUR
AU - Aparajita Dasgupta
AU - M. W. Wong
TI - Spectral theory of SG pseudo-differential operators on $L^{p}(ℝⁿ)$
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 2
SP - 185
EP - 197
AB - To every elliptic SG pseudo-differential operator with positive orders, we associate the minimal and maximal operators on $L^{p}(ℝⁿ)$, 1 < p < ∞, and prove that they are equal. The domain of the minimal ( = maximal) operator is explicitly computed in terms of a Sobolev space. We prove that an elliptic SG pseudo-differential operator is Fredholm. The essential spectra of elliptic SG pseudo-differential operators with positive orders and bounded SG pseudo-differential operators with orders 0,0 are computed.
LA - eng
KW - pseudo-differential operators; ellipticity; minimal and maximal operators; Fredholm operators; essential spectra; indices
UR - http://eudml.org/doc/284819
ER -

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