{"product_id":"analysis-iv-linear-and-boundary-integral-equations-von-v-g-mazya-s-m-nikolskii-hrsg","title":"Analysis IV","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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642634918\"\u003e\u003ch3\u003eLinear and Boundary Integral Equations\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642634918","offer_id":39444845592669,"sku":"9783642634918","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/d18672e0-2e0a-4174-9f0a-6f3dcac821a3.jpg?v=1772085974","url":"https:\/\/shop.autorenwelt.de\/en\/products\/analysis-iv-linear-and-boundary-integral-equations-von-v-g-mazya-s-m-nikolskii-hrsg","provider":"Autorenwelt Shop","version":"1.0","type":"link"}