## Global Pseudo-differential Calculus on Euclidean SpacesThis book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics. |

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### Contents

1 | |

8 | |

Chapter 1 Global PseudoDifferential Calculus
| 15 |

Chapter 2 ΓPseudoDifferential Operators and HPolynomials
| 67 |

Chapter 3 GPseudoDifferential Operators
| 129 |

Chapter 4 Spectral Theory
| 152 |

### Other editions - View all

Global Pseudo-differential Calculus on Euclidean Spaces Fabio Nicola,Luigi Rodino No preview available - 2010 |

### Common terms and phrases

a e S(M Anti-Wick apply aſa Assume the strong asymptotic expansion B1 H Banach space bounded bounded operator Buzano calculus compact consider convergent defined Definition denote differential operators eaſists eigenvalues elliptic symbol equation equivalent estimates example exponential decay formula Fourier transform Fredholm Fredholm operator function G-elliptic given global regularity Hence Hilbert space hypoelliptic implies integral kernel Lemma Let a e linear Lº(R LP(R Moreover multi-quasi-elliptic Newton polyhedron norm observe obtain operator with symbol parametrix polynomial positive constant proof of Theorem Proposition prove pseudo-differential operator quantization regularizing operators result right-hand side Rodino Rºº S(Rd satisfying Schwartz Schwartz functions Section self-adjoint operator sequence short-time Fourier transform Sobolev spaces solutions strong uncertainty principle trace-class u e S(R Weyl quantization Weyl symbol