Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
5 sonuçtan 1-3 arası sonuçlar
Sayfa 1
... belong . With applications of integral geometry to the study of linearized problems in mind , the most natural one for our purposes is the space с of contin- uous functions . Throughout the following we shall assume the solutions of ...
... belong . With applications of integral geometry to the study of linearized problems in mind , the most natural one for our purposes is the space с of contin- uous functions . Throughout the following we shall assume the solutions of ...
Sayfa 21
... belong to the set V of functions satisfying the following conditions : 1. For each v ( x , r ) EV , the functions Mv ( k = 0,1 , ... ) are continuous . ∞ 2 . Σ max | Mxv \ x = 0 < k = 0 r 3. Each v ( x , r ) EV satisfies inequality ( 8 ) ...
... belong to the set V of functions satisfying the following conditions : 1. For each v ( x , r ) EV , the functions Mv ( k = 0,1 , ... ) are continuous . ∞ 2 . Σ max | Mxv \ x = 0 < k = 0 r 3. Each v ( x , r ) EV satisfies inequality ( 8 ) ...
Sayfa 53
... belong to L1 ( D ) . We take FOURIER transforms in ( 5 ) with respect to in this connection equation ( 7 ) of Sec.1 , Chapt.4 . Equation ( 5 ) then assumes the form ( 6 ) ∞ 1 81 ∞ b ( 5 , n ) e F1 ( w1ow 2 ) = 1 2 X1 and X2 using ...
... belong to L1 ( D ) . We take FOURIER transforms in ( 5 ) with respect to in this connection equation ( 7 ) of Sec.1 , Chapt.4 . Equation ( 5 ) then assumes the form ( 6 ) ∞ 1 81 ∞ b ( 5 , n ) e F1 ( w1ow 2 ) = 1 2 X1 and X2 using ...
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
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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