Multidimensional Inverse Problems for Differential EquationsM. M. Lavrentiev, Mikhail Mikhailovich Lavrent£ev, Vladimir Gavrilovich Romanov, V. G. Romanov, V. G. Vasiliev Springer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
8 sonuçtan 1-3 arası sonuçlar
Sayfa 7
... inequality ( 18 ) Iv ( p , E ) 2π α . • Properties 10-30 follow in a trivial way from the corresponding pro- perties of the functions u ( r , ) and equations ( 14 ) , ( 14 ' ) and ( 15 ) . Only inequality ( 18 ) remains to be proved ...
... inequality ( 18 ) Iv ( p , E ) 2π α . • Properties 10-30 follow in a trivial way from the corresponding pro- perties of the functions u ( r , ) and equations ( 14 ) , ( 14 ' ) and ( 15 ) . Only inequality ( 18 ) remains to be proved ...
Sayfa 18
... inequality ( 14 ) holds will be v ( p , a ) of U under the mapping ( 2 ) will labeled U. The set of images be denoted by V. Theorem 6 : The set V possesses the following properties : 1o . For each v ( p , a ) , the functions M1v ( k = 0 ...
... inequality ( 14 ) holds will be v ( p , a ) of U under the mapping ( 2 ) will labeled U. The set of images be denoted by V. Theorem 6 : The set V possesses the following properties : 1o . For each v ( p , a ) , the functions M1v ( k = 0 ...
Sayfa 42
... inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , x ) | < απ 2.2 + ო 2 2 t = n - y1 p2 = a2x 2.2 + 3 2 , , F1 ( w , t ) = F ( w , t + y 1 ) = F11 ( w , t ) + 1F12 ( w , t ) , ( 10a ) 11 У 1Р Q1 ( w , p ) ...
... inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , x ) | < απ 2.2 + ო 2 2 t = n - y1 p2 = a2x 2.2 + 3 2 , , F1 ( w , t ) = F ( w , t + y 1 ) = F11 ( w , t ) + 1F12 ( w , t ) , ( 10a ) 11 У 1Р Q1 ( w , p ) ...
İçindekiler
Generalization to Analytic Curves | 10 |
On the Problem of Determining a Function from Its Mean | 19 |
Two Formulations of the Linearized Inverse Problem | 28 |
Telif Hakkı | |
2 diğer bölüm gösterilmiyor
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 belong boundary conditions CAUCHY data chapter coefficients consider const continuous function corresponding cosy Denote derive determining a function differential equation Dokl domain earth's ellipses ellipsoid of revolution exists 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 linearized inverse problem mean values multidimensional inverse problems Nauk SSSR obtain operator L defined parameters polar potential theory problem for equation problem of determining Problems for Differential R₁ R₂ right-hand side ROMANOV satisfies second kind solution to equation STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation waves wxxx