AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We study the domains of absolute convergence of monomial expansions of holomorphic functions on Banach sequence spaces. We first show that, in every complex Banach sequence space $X$, each point outside the closed linear span of the coordinate unit vectors admits a continuous quadratic polynomial whose monomial expansi...
We prove dimension-free higher-order Sobolev norm estimates on open convex subsets of $\mathbb{R}^n$ with respect to Gaussian measure and use them to obtain norm equivalence on nonempty open convex subsets of $\ell^2$ endowed with a nondegenerate Gaussian measure. To the best of our knowledge, this is the first such eq...
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