{"product_id":"analysis-iv-v-g-mazya-9783642634918","title":"Analysis IV: Linear and Boundary Integral Equations","description":"A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integralequations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e V. G. Maz'ya\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3642634915\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783642634918\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/01\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 236\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.78lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.52d","brand":"V. G. Maz'ya","offers":[{"title":"Paperback","offer_id":48487000899839,"sku":"9783642634918","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_861fd388-8580-44a4-b268-9a8859860898.jpg?v=1778057690","url":"https:\/\/www.whiterainbookhouse.com\/products\/analysis-iv-v-g-mazya-9783642634918","provider":"WR Book House","version":"1.0","type":"link"}