Mean-Value Formula for a Hyperbolic Equation with a Factorizable Operator
نویسندگان
چکیده
A mean-value formula for a linear partial differential hyperbolic equation with an operator splitting into first-order factors is obtained. This can be interpreted as extension of the Ásgeirsson principle.
منابع مشابه
A mean value formula for elliptic curves
It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate.
متن کاملOn Initial Boundary Value Problem with Dirichlet Integral Conditions for a Hyperbolic Equation with the Bessel Operator
We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formu...
متن کاملThe spherical mean value operator with centers on a sphere
Let B represent the ball of radius ρ in Rn and S its boundary; consider the map M : C∞ 0 (B) → C∞(S × [0,∞)) where (Mf)(p, r) = 1 ωn−1 ∫ |θ|=1 f(p+ rθ) dθ represents the mean value of f on a sphere of radius r centered at p. We summarize and discuss the results concerning the injectivity of M, the characterization of the range of M, and the inversion of M. There is a close connection between me...
متن کاملMean Value Problems of Flett Type for a Volterra Operator
In this note we give a generalization of a mean value problem which can be viewed as a problem related to Volterra operators. This problem can be seen as a generalization of a result concerning the zeroes of a Volterra operator in the Banach space of continuous functions with null integral on a compact interval.
متن کاملOn some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06184-1