{"product_id":"cegrell-urban-capacities-in-complex-analysis-9783528063351","title":"Capacities in Complex Analysis","description":"The 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.","brand":"Vieweg+Teubner Verlag","offers":[{"title":"Default Title","offer_id":53683164315990,"sku":null,"price":0.0,"currency_code":"EUR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0925\/5829\/5382\/files\/product_image_9783528063351_1.jpg?v=1778851824","url":"https:\/\/www.momoxbooks.com\/products\/cegrell-urban-capacities-in-complex-analysis-9783528063351","provider":"momoxbooks","version":"1.0","type":"link"}