Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
15 sonuçtan 1-3 arası sonuçlar
Sayfa 12
... solution we seek for ( 9 ) has to be bounded . But since for -λ p → 00 if C 0 , we can assert that λ < 0 , Cp tends to infinity as any bounded solution to ( 9 ) is unique . If we apply L to equation ( 3 ) k times in succession , we let ...
... solution we seek for ( 9 ) has to be bounded . But since for -λ p → 00 if C 0 , we can assert that λ < 0 , Cp tends to infinity as any bounded solution to ( 9 ) is unique . If we apply L to equation ( 3 ) k times in succession , we let ...
Sayfa 44
... solution to ( 16 ) be a certain function f ( x , y ) € L , ( D ) , D = { -∞ < x < ∞ ; 0 < y < ∞ ) . We can then represent the unique solution to equation ( 17 ) by means of formula ( 12 ) . On inverting the FOURIER transform ( 13 ) ...
... solution to ( 16 ) be a certain function f ( x , y ) € L , ( D ) , D = { -∞ < x < ∞ ; 0 < y < ∞ ) . We can then represent the unique solution to equation ( 17 ) by means of formula ( 12 ) . On inverting the FOURIER transform ( 13 ) ...
Sayfa 54
... unique solution ( almost everywhere ) in the class of absolutely integrable functions . The solution may be represented by ( 10 ) b ( 5 , n ) = r ( u , n ) e luau . 2π S Thus we have proved the following uniqueness theorem for equation ...
... unique solution ( almost everywhere ) in the class of absolutely integrable functions . The solution may be represented by ( 10 ) b ( 5 , n ) = r ( u , n ) e luau . 2π S Thus we have proved the following uniqueness theorem for equation ...
Diğer baskılar - Tümünü görüntüle
Multidimensional Inverse Problems for Differential Equations M. M. Lavrentiev,V. G. Romanov,V. G. Vasiliev Metin Parçacığı görünümü - 1970 |
Sık kullanılan terimler ve kelime öbekleri
absolutely integrable functions Akad analytic function belong boundary conditions CAUCHY data chapter coefficients consider const continuous function coordinates corresponding cosk Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution expression family of curves following theorem function u(r fundamental solution given GREEN'S function half-plane half-space HÖLDER condition hyperplane inequality 18 integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inversion formula kernel Lavrentiev linearized inverse problem multidimensional inverse problems Nauk SSSR obtain parameters polar potential theory problem for equation problem of determining Problems for Differential R₁ R₂ right-hand side ROMANOV satisfies second kind SM,t solution to equation take FOURIER transforms telegraph equation two-parameter family unique solution uniqueness theorem unit circle variables VOLTERRA equation waves wxxx