Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
5 sonuçtan 1-3 arası sonuçlar
Sayfa 4
... moments on each ellipse . Since u ( x , s ) is an even function of s , it is uniquely de- termined by these moments . In other words , if a solution to equation ( 4 ) exists , it is unique . We next consider how relations ( 8 ) may be ...
... moments on each ellipse . Since u ( x , s ) is an even function of s , it is uniquely de- termined by these moments . In other words , if a solution to equation ( 4 ) exists , it is unique . We next consider how relations ( 8 ) may be ...
Sayfa 10
... moments for ( 246 ) 11 12 • X2 X1 Su ( x , s ) x11.x2 ... λη dw , Xn u ( x , s ) : So , t = 0,1,2 , ... ) , ( 1 = 1,2 , ... , n ) 1 where So , t is a sphere of radius t with center at the origin . These moments determine our even ...
... moments for ( 246 ) 11 12 • X2 X1 Su ( x , s ) x11.x2 ... λη dw , Xn u ( x , s ) : So , t = 0,1,2 , ... ) , ( 1 = 1,2 , ... , n ) 1 where So , t is a sphere of radius t with center at the origin . These moments determine our even ...
Sayfa 11
... moments of u ( r , 4 ) on each circle S ' P , o ' Expanding ( ε , n ) in a series with respect to n and substituting it in formula ( 2 ) , we obtain ( 3 ) v ( p , c ) = 00 k [ € * ax ( e ) Vk ( p , e ) , k = 0 u ( r , 4 ) cosk4a4 ...
... moments of u ( r , 4 ) on each circle S ' P , o ' Expanding ( ε , n ) in a series with respect to n and substituting it in formula ( 2 ) , we obtain ( 3 ) v ( p , c ) = 00 k [ € * ax ( e ) Vk ( p , e ) , k = 0 u ( r , 4 ) cosk4a4 ...
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
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