impaction
发表于 2025-3-30 11:20:05
A Priori Estimates, is solvable. Looking from the point of view of the theory of equations, the content of (7.1) is: if x is any solution of equation (A), the it satisfies .. This is the reason why such estimates are known under the name of ..
Glycogen
发表于 2025-3-30 14:33:05
Linear Transformations of Equations,we must proceed with a certain amount of caution. If the operator B is not defined everywhere on F, then the solutions of equation (A) corresponding to right-hand sides y ∉ υ(B) are not in the set of all solutions of equation (BA).
cornucopia
发表于 2025-3-30 16:47:27
Equations with Finite Defect,it will have at most n steps: the functionals Φ.. are linearly independent (if . for all z ∈ ., then taking successively z = u., z = u.,..., we obtain c. = 0, c. = 0,...) and are all in .. In fact, the number of steps is exactly n. Indeed, if the process terminates at the m-th step, then one can write every element z ∈ . as ..
漂亮才会豪华
发表于 2025-3-31 00:23:23
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Chandelier
发表于 2025-3-31 04:42:59
https://doi.org/10.1007/978-1-4684-8068-9BASIC; DEX; Factor; THE; banach spaces; differential equation; form; function; functional analysis; integral;
AMBI
发表于 2025-3-31 05:31:40
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艺术
发表于 2025-3-31 09:39:27
The Equation Adjoint to the Factored Equation,s its value in Ẽ*. Using the general theorems, Ẽ* = .(A)., where the orthogonal complement is taken in E* Let us show that υ(Ã*) and υ(A*) are the same. Indeed, let g ∈ υ(A*) ⊂ F*, i.e., the functional g(Ax) is bounded on υ(A): ..
个人长篇演说
发表于 2025-3-31 17:03:02
Equations with Operators Which Act in a Single Space, this allows us to introduce a new important characteristic of equation (A). Namely, let W. (A) be the set of all elements x such that A.x = θ for some k > 0. This set is a linear manifold: if A.x. = θ and A.x. = θ, then ..
iodides
发表于 2025-3-31 20:44:55
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Fantasy
发表于 2025-4-1 01:01:17
Undetermined Equations,{θ}, then equation (A,B) is manifestly not uniquely solvable. Indeed, let Ax. = Bu. (x. ∈ P(A), U. ∈ .(B)). Then the pair (X.,-u.) is a solution of the homogeneous equation (A,B). Due to such behaviour, it is natural to say that equation (A,B) is ..