Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
8 sonuçtan 1-3 arası sonuçlar
Sayfa 7
... inequality ( 18 ) Iv ( p , e ) < 2π α • Properties 10-3 ° follow in a trivial way from the corresponding pro- perties of the functions u ( r , ) u ( r , ) and equations ( 14 ) , ( 14 ' ) and ( 15 ) . Only inequality ( 18 ) remains to be ...
... inequality ( 18 ) Iv ( p , e ) < 2π α • Properties 10-3 ° follow in a trivial way from the corresponding pro- perties of the functions u ( r , ) u ( r , ) and equations ( 14 ) , ( 14 ' ) and ( 15 ) . Only inequality ( 18 ) remains to be ...
Sayfa 18
... inequality ( 14 ) holds will be v ( p , a ) of U under the mapping ( 2 ) will Theorem 6 : The set V possesses the following properties : 10. For each v ( p , a ) , the functions MV ( k = 0 , ± 1 , ± 2 , ... ) are continuous . 2o . For ...
... inequality ( 14 ) holds will be v ( p , a ) of U under the mapping ( 2 ) will Theorem 6 : The set V possesses the following properties : 10. For each v ( p , a ) , the functions MV ( k = 0 , ± 1 , ± 2 , ... ) are continuous . 2o . For ...
Sayfa 42
... inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p , = F ( w , t ) + 1F12 ...
... inequality into ( 9 ) , we finally obtain ( 10 ) Introduce the notation | G ( w , λ ) | < απ 2,2 2 a - λ + w t = n - Ꭹ . p2 = a ( 10a ) 1 F1 ( w , t ) = F ( w2t + y 1 ) y1p Q1 ( w , p ) e = Q ( w , 11 √ 2 2 31 p , = F ( w , t ) + 1F12 ...
İçindekiler
CHAPTER | 1 |
Problem of Determining a Function inside a Circle from | 13 |
On the Problem of Determining a Function from Its Mean | 19 |
Telif Hakkı | |
4 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 |
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 analytic function arbitrary belong boundary conditions CAUCHY data chapter consider const continuous function corresponding Denote derive determining a function differential equation 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 HOLDER condition hyperplane inequality 16 initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation inverse kinematic inverse kinematic problem inverse problem inversion formula kernel L₁ linearized inverse problem M₁ mean values multidimensional inverse problems n₁ obtain operator L defined parameters polar problem for equation problem of determining Q₂ R₁ R₂ relations right-hand side second kind SM,t solution to equation take FOURIER transforms telegraph equation travel-times two-parameter family u₁ M,M,t unique solution uniqueness theorem unit circle values over spheres variables VOLTERRA equation waves wxxx θε ду эф