Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subelliptic pseudo-differential operators and Fourier integral operators
  on compact Lie groups   In this work we extend the theory of global pseudo-differential operators on
compact Lie groups to a subelliptic context. More precisely,given a compact Lie
group $G$, and the sub-Laplacian $\mathcal{L}$ associated to a system of vector
fields satisfying the H\"ormander condition, we introduce a (subelliptic)
pseudo-differential calculus associated to $\mathcal{L},$ based on the
matrix-valued quantisation process developed in [111]. This theory will be
developed as follows. First, we will investigate the singular kernels of this
calculus, estimates of Lp-Lp, H1-L1, $L^\infty$-BMO type and also the weak
(1,1) boundedness of these subelliptic H\"ormander classes. Between the
obtained estimates we prove subelliptic versions of the celebrated sharp
Fefferman Lp-theorem and the Calder\'on-Vaillancourt theorem. The obtained
estimates will be used to establish the boundedness of subelliptic operators on
subelliptic Sobolev and Besov spaces. We will investigate the ellipticity, the
construction of parametrices, the heat traces and the regularisation of traces
for the developed subelliptic calculus. A subelliptic global functional
calculus will be established as well as a subelliptic version of Hulanicki
theorem. This subelliptic functional calculus will be used to prove a
subelliptic version of the G\r{a}rding inequality, which we also use to study
the global solvability for a class of subelliptic pseudo-differential problems.
Finally, by using both, the matrix-valued symbols and also the notion of
matrix-valued phases we study the $L^2$-boundedness of global Fourier integral
operators. The approach established in characterising our subelliptic
H\"ormander classes (by proving that the definition of these classes is
independent of certain parameters) will be also applied in order to
characterise the global H\"ormander classes on arbitrary graded Lie groups
developed in [66].

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg