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Quantum gravity: are we there yet? [PDF]
Philos Trans A Math Phys Eng SciMajid S.
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Nonregular Pseudo-Differential Operators
Zeitschrift für Analysis und ihre Anwendungen, 1996We study the boundedness properties of pseudo-differential operators a(x, D) and their adjoints a(x, D)* with symbols in a certain vector-valued Besov space on Besov
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Pseudo‐differential operator in quaternion space
Mathematical Methods in the Applied Sciences, 2023This paper introduces the quaternion Schwarz type space, and quaternion linear canonical transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo‐differential operator (QPDO) associated with QLCT is described. Some of its characteristics, including estimates, boundedness, and integral representation in quaternion Sobolev ...
Manab Kundu, Akhilesh Prasad
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1997
The theory of pseudo-differential operators is one of the most important toolsin modern mathematics. It has found important applications in many mathematicaldevelopments. It was used in a crucial way in the proof of the Atiyah-SingerIndex theorem in [AtSi] and in the regularity of elliptic differential equations.In the theory of several complex ...
Yuri V. Egorov, Bert-Wolfgang Schulze
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The theory of pseudo-differential operators is one of the most important toolsin modern mathematics. It has found important applications in many mathematicaldevelopments. It was used in a crucial way in the proof of the Atiyah-SingerIndex theorem in [AtSi] and in the regularity of elliptic differential equations.In the theory of several complex ...
Yuri V. Egorov, Bert-Wolfgang Schulze
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Communications on Pure and Applied Mathematics, 1965
Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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1985
We will now turn to a class of operators which — roughly speaking (details below) — are locally presentable in the form $$\left( {Pu} \right)\left( x \right)\,: = \int {ei p\left( {x,\varepsilon } \right)} \mathop u\limits^ \wedge \left( \varepsilon \right)d\varepsilon$$ where $$ \hat u\left( x \right): = \int {e^{ - i\left\langle {x,\xi }
B. Booss, D. D. Bleecker
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We will now turn to a class of operators which — roughly speaking (details below) — are locally presentable in the form $$\left( {Pu} \right)\left( x \right)\,: = \int {ei p\left( {x,\varepsilon } \right)} \mathop u\limits^ \wedge \left( \varepsilon \right)d\varepsilon$$ where $$ \hat u\left( x \right): = \int {e^{ - i\left\langle {x,\xi }
B. Booss, D. D. Bleecker
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2010
The main purpose of this chapter is to obtain the boundedness on \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) of all pseudo-differential operators of type (1,1) with inhomogeneous symbols. The smooth molecular decomposition characterizations of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) play an important role in this chapter.
Wen Yuan, Winfried Sickel, Dachun Yang
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The main purpose of this chapter is to obtain the boundedness on \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) of all pseudo-differential operators of type (1,1) with inhomogeneous symbols. The smooth molecular decomposition characterizations of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) play an important role in this chapter.
Wen Yuan, Winfried Sickel, Dachun Yang
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Annali di Matematica Pura ed Applicata, 1972
We present here a number of results on some aspects of Kohn-Nirenberg's theory of pseudo-differential operators. We hope that some parts of Kohn-Nirenberg's paper[1] are presented here in a more detailed and explicit form; this could help a larger audience to understand their ideas and methods.
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We present here a number of results on some aspects of Kohn-Nirenberg's theory of pseudo-differential operators. We hope that some parts of Kohn-Nirenberg's paper[1] are presented here in a more detailed and explicit form; this could help a larger audience to understand their ideas and methods.
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G-Pseudo-Differential Operators
2010As in Chapter 2, the basic example here is a partial differential operator with polynomial coefficients in ℝ d , that is $$ P = \sum {c_{\alpha \beta } x^\beta D^\alpha } , $$ wherein the sum (α,β) ∈ ℕ d × ℕ d runs over a finite subset of indices.
Fabio Nicola, Luigi Rodino
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