Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almansi Theorems in Umbral Clifford Analysis and the Quantum Harmonic
  Oscillator   We introduce the Umbral calculus into Clifford analysis starting from the
abstract of the Heisenberg commutation relation $[\frac{d}{dx}, x] = {\bf id}$.
The Umbral Clifford analysis provides an effective framework in continuity and
discreteness.
  In this paper we consider functions defined in a star-like domain $\Omega
\subset \BR^n$ with values in the Umbral Clifford algebra $C\ell_{0,n}'$ which
are Umbral polymonogenic with respect to the (left) Umbral Dirac operator $D'$,
i.e. they belong to the kernel of $(D')^k$. We prove that any polymonogenic
function $f$ has a decomposition of the form $$f=f_1+ x'f_2 + ... +
(x')^{k-1}f_k,$$ where $x'=x'_1e_1 + ... + x'_ne_n$ and $f_j, j=1,..., k,$ are
Umbral monogenic functions. As examples, this result recoveries the continuous
version of the classical Almansi theorem for derivatives and establishes the
discrete version of Almansi theorem for difference operator. The approach also
provides a similar result in quantum field about Almansi decomposition related
to Hamilton operators.
  Some concrete examples will presented for the discrete analog version of
Almansi Decomposition and for the quantum harmonic oscillator.

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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con