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تسجيل مستخدم جديدOn Lisbon integrals
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تأليف
Daniel Barlet
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We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space $mathbb{C}^k$ of unitary polynomials $P_s(z)$ where $sinmathbb{C}^k$ and $zin mathbb{C}$, $s_i$ identified to the $i-$th symmetric function of the roots of $P_s(z)$. We completely determine the $mathcal{D}$-modules (or systems of partial differential equations) the Lisbon Integrals satisfy and prove that they are their unique global solutions. If we specify a holomorphic function $f$ in the $z$-variable, our construction induces an integral transform which associates a regular holonomic module quotient of the sub-holonomic module we computed. We illustrate this correspondence in the case of a $1$-parameter family of exponentials $f_t(z) = exp(t z)$ with $t$ a complex parameter.
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