{"product_id":"capacities-in-complex-analysis-9783528063351","title":"Capacities in Complex Analysis","description":"\u003cp\u003e • Author(s): Urban Cegrell\u003cbr\u003e • Publisher: Vieweg+teubner Verlag\u003cbr\u003e • Publisher Imprint: Vieweg+teubner Verlag\u003cbr\u003e • BISAC: Programming - Algorithms\u003c\/p\u003e\u003cp\u003eThe purpose of this book is to study plurisubharmonic and analytic functions in n using capacity theory. The case n=l has been studied for a long time and is very well understood. The theory has been generalized to mn and the results are in many cases similar to the situation in . However, these results are not so well adapted to complex analysis in several variables - they are more related to harmonic than plurihar- monic functions. Capacities can be thought of as a non-linear generali- zation of measures; capacities are set functions and many of the capacities considered here can be obtained as envelopes of measures. In the mn theory, the link between functions and capa- cities is often the Laplace operator - the corresponding link in the n theory is the complex Monge-Ampere operator. This operator is non-linear (it is n-linear) while the Laplace operator is linear. This explains why the theories in mn and n differ considerably. For example, the sum of two harmonic functions is harmonic, but it can happen that the sum of two plurisubharmonic functions has positive Monge-Ampere mass while each of the two functions has vanishing Monge-Ampere mass. To give an example of similarities and differences, consider the following statements. Assume first that is an open subset VIII of n and that K is a closed subset of Q. Consider the following properties that K mayor may not have.\u003c\/p\u003e","brand":"Vieweg+teubner Verlag","offers":[{"title":"Paperback","offer_id":46893939097751,"sku":"9783528063351","price":3776.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783528063351.webp?v=1770320078","url":"https:\/\/atlanticbooks.com\/products\/capacities-in-complex-analysis-9783528063351","provider":"Atlantic Books","version":"1.0","type":"link"}