{"product_id":"optimal-domain-and-integral-extension-of-operators-acting-in-frechet-function-spaces-paperback","title":"Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eBettina Blaimer\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eIt is known that a continuous linear operator T defined on a Banach function space X(mu) (over a finite measure space (Omega, igma, mu) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(mu) and the operator T this optimal domain coincides with L\u003csup\u003e1\u003c\/sup\u003e(m\u003csub\u003eT\u003c\/sub\u003e), the space of all functions integrable with respect to the vector measure m\u003csub\u003eT\u003c\/sub\u003e associated with T, and the optimal extension of T turns out to be the integration operator I\u003csub\u003em\u003c\/sub\u003e\u003csub\u003eT\u003c\/sub\u003e. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Frechet function spaces X(mu) (this time over a sigma-finite measure space (Omega, igma, mu). It is shown that under similar assumptions on X(mu) and T as in the case of Banach function spaces the so-called \"optimal extension process\" also works for this altered situation. In a further step the newly gained results are applied to four well-known operators defined on the Frechet function spaces L\u003csup\u003ep-\u003c\/sup\u003e([0,1]) resp. L\u003csup\u003ep-\u003c\/sup\u003e(G) (where G is a compact Abelian group) and L\u003csup\u003ep\u003c\/sup\u003e\u003csub\u003eloc-\u003c\/sub\u003e\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 137\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.4 x 9.38 x 6.55 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 30, 2017\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":46661627216069,"sku":"9783832545574","price":105.28,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0757\/6718\/5605\/files\/xGgF7Iy2il9783832545574.webp?v=1785907693","url":"https:\/\/selloorium.com\/products\/optimal-domain-and-integral-extension-of-operators-acting-in-frechet-function-spaces-paperback","provider":"Selloorium","version":"1.0","type":"link"}