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Showing 1 to 4 of 4 for “"Plurisubharmonic Functions"”.
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EXTENSION OF PLURISUBHARMONIC FUNCTIONS AND DYNAMICS OF POLYNOMIAL MAPPINGS
… P^n$. Coman-Guedj-Zeriahi proved that any plurisubharmonic function with logarithmic growth on $X$ extends to a plurisubharmonic function with logarithmic growth on $\mathbb C^n$ when the germs $(\overline X,a)$ in $\mathbb P^n$ are irreducible for all $a\in \overline X\setminus X.$ In this …
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Higher dimensional fractal uncertainty
… which allows us to construct band-limited functions that decay rapidly on line porous sets. To prove this theorem, we first explicitly construct certain plurisubharmonic functions on Cᵈ. Then, following Bourgain, we use Hörmander’s L² theory for the ¯∂ equation to construct band-limited …
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On some maximal convergence theorems for real analytic functions in R^N
… \\ $[$Sic62$]$ Siciak, J., {\it On some extremal functions and their applications in the theory of analytic functions of several complex variables}, Trans. Amer. Math. Soc. (1962), {\bf 105}, 322--357. \\ $[$Sic81$]$ Siciak, J., {\it Extremal plurisubharmonic functions in $\mathbb{C}^N$}, Ann. …
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Lelong Numbers and Geometric Properties of Upper Level Sets of Currents on Projective Space
<p>Let $T$ be a positive closed bidegree $(p,p)$ current in $\mathbb{P}^n$. In this thesis, our goal is to understand more about the geometric properties of the sets of highly singular points of the current $T$. Lelong numbers will be the main tool used for determining how singular a point of a …