Multidimensional Inverse Problems for Differential EquationsSpringer, 21 Ara 1970 - 59 sayfa |
Kitabın içinden
11 sonuçtan 1-3 arası sonuçlar
Sayfa 41
... take FOURIER transforms in equation ( 6 ) with respect to X under the above assumptions on f ( x , y ) . From ( 7 ) it follows that the kernel of the integral equation ( 6 ) is an absolutely integrable function . Then by the theorem ...
... take FOURIER transforms in equation ( 6 ) with respect to X under the above assumptions on f ( x , y ) . From ( 7 ) it follows that the kernel of the integral equation ( 6 ) is an absolutely integrable function . Then by the theorem ...
Sayfa 44
... take FOURIER transforms with respect to x , we wind up with ( 17 ) 2. 2 -na + w G ( w , λ ) = Introduce the notation 2,2 2 p2 = a2x2 + w2 , 2 ( 17a ) 1 2,2 2 F ( w , n ) dn = a - λ tw G ( w , λ ) ∞ П g ( x , λ ) e -iwxdx · # ŠE ( X , A ) ...
... take FOURIER transforms with respect to x , we wind up with ( 17 ) 2. 2 -na + w G ( w , λ ) = Introduce the notation 2,2 2 p2 = a2x2 + w2 , 2 ( 17a ) 1 2,2 2 F ( w , n ) dn = a - λ tw G ( w , λ ) ∞ П g ( x , λ ) e -iwxdx · # ŠE ( X , A ) ...
Sayfa 53
... 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 ) - £ ༦ , * ༧a ) c £ - ཀ t ...
... 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 ) - £ ༦ , * ༧a ) c £ - ཀ t ...
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