{"product_id":"9783319676111","title":"Lecture Notes in Mathematics: Non-Effectively Hyperbolic Characteristics","description":"\u003ch1\u003eLecture Notes in Mathematics: Non-Effectively Hyperbolic Characteristics\u003c\/h1\u003e \u003ch2\u003eNishitani, Tatsuo\u003c\/h2\u003e \u003cp\u003eCombining geometrical and microlocal tools, this monograph gives detailed proofs of many well\/ill-posed results related to the Cauchy problem for differential operators with non-effectively hyperbolic double characteristics. Previously scattered over numerous different publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well\/ill-posedness of the Cauchy problem.\u003c\/p\u003e\u003cdiv\u003e\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eA doubly characteristic point of a differential operator P of order m (i.e. one where Pm = dPm = 0) is effectively hyperbolic if the Hamilton map FPm has real non-zero eigen values. When the characteristics are at most double and every double characteristic is effectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003eIf there is a non-effectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between −Pµj and Pµj, where iµj are the positive imaginary eigenvalues of FPm . Moreover, if 0 is an eigenvalue of FPm with corresponding 4 × 4 Jordan block, the spectral structure of FPm is insufficient to determine whether the Cauchy problem is well-posed and the behavior of bicharacteristics near the doubly characteristic manifold plays a crucial role.\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-11-26\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319676111\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-67612-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 213\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45369833816204,"sku":"9783319676111","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319676111.jpg?v=1775675641","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319676111","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}