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
7 sonuçtan 1-3 arası sonuçlar
Sayfa 15
... respect to P are additional restrictions on the density with which the curves of the family cover the unit circle . Thus suppose that the integrals of u ( r , Y ) with respect to arclength are known on the family of curves satisfying ...
... respect to P are additional restrictions on the density with which the curves of the family cover the unit circle . Thus suppose that the integrals of u ( r , Y ) with respect to arclength are known on the family of curves satisfying ...
Sayfa 41
... respect to X and using the relation ( see [ 7 ] ) ( 7 ) Ko [ b ( c2 + t 2 cos ut dt = 2√62 + 1 ਸ਼ਣ π we obtain ( 7a ) Јесо 2,2 , + = with 2.2 a - λ -Y1 3 2 1 / 1252 + 02 ( 2 ( x + 2 ) π√2π -e - Inty1 g ( x , 1 ) e -iwx dx 3 2.2 . a ...
... respect to X and using the relation ( see [ 7 ] ) ( 7 ) Ko [ b ( c2 + t 2 cos ut dt = 2√62 + 1 ਸ਼ਣ π we obtain ( 7a ) Јесо 2,2 , + = with 2.2 a - λ -Y1 3 2 1 / 1252 + 02 ( 2 ( x + 2 ) π√2π -e - Inty1 g ( x , 1 ) e -iwx dx 3 2.2 . a ...
Sayfa 44
... respect to X , we wind up with ( 17 ) 2 2 2,2 2 -na + w F ( w , n ) an = 1 √ a2x2 + w2 G ( w2 X ) ∞ 1 G ( w , λ ) = # √ g ( x , λ ) e -1wxdx . Introduce the notation 2 p2 = a2x2 + w2 , 2,2 12 ( 17a ) • ( p , w ) = 1 pG ( w , 1 p π а ...
... respect to X , we wind up with ( 17 ) 2 2 2,2 2 -na + w F ( w , n ) an = 1 √ a2x2 + w2 G ( w2 X ) ∞ 1 G ( w , λ ) = # √ g ( x , λ ) e -1wxdx . Introduce the notation 2 p2 = a2x2 + w2 , 2,2 12 ( 17a ) • ( p , w ) = 1 pG ( w , 1 p π а ...
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