Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
26 sonuçtan 1-3 arası sonuçlar
Sayfa 5
... functions for which we have proved the uniqueness of the reconstruc- ted function from its integrals over ellipses . Namely , we shall con- sider functions u ( r , ) satisfying the following conditions : is an 10. each u ( r , Y ) is a ...
... functions for which we have proved the uniqueness of the reconstruc- ted function from its integrals over ellipses . Namely , we shall con- sider functions u ( r , ) satisfying the following conditions : is an 10. each u ( r , Y ) is a ...
Sayfa 17
... ( r , s ) = ак Formula ( 10 ) implies that S in D together with ( 10a ) π de . Ry ( r , rts + rs cose ) de . Q ( r , s ) is a continuous function of r and a r - s ( r , s ) . In addition , = ask Qx ( s , s ) ... functions u ( r , Y ) - · - 17 -
... ( r , s ) = ак Formula ( 10 ) implies that S in D together with ( 10a ) π de . Ry ( r , rts + rs cose ) de . Q ( r , s ) is a continuous function of r and a r - s ( r , s ) . In addition , = ask Qx ( s , s ) ... functions u ( r , Y ) - · - 17 -
Sayfa 18
... ( Mxv ) eik k = -∞ By conditions 1 ° and 2 ° the series converges to a continuous function u ( r , Y ) for which the functions efficients . Hence by condition 2 ° it belongs to M1 v ' k are its FOURIER co- U. On the basis of u ( r , ) , - - ...
... ( Mxv ) eik k = -∞ By conditions 1 ° and 2 ° the series converges to a continuous function u ( r , Y ) for which the functions efficients . Hence by condition 2 ° it belongs to M1 v ' k are its FOURIER co- U. On the basis of u ( r , ) , - - ...
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 |
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