Characterization of the Homogeneous Polynomials P for Which (p +q)(d) Admits a Continuous Linear Right Inverse for All Lower Order Perturbations Q
نویسندگان
چکیده
Those homogeneous polynomials P are characterized for which for arbitrary lower order polynomials Q the partial differential operator (P+Q)(D) admits a continuous linear right inverse if regarded as an operator from the space of all C∞functions on R into itself. It is shown that P has this property if and only if P is of principal type and real up to a complex constant and has no elliptic factor.
منابع مشابه
Perturbation of Differential Operators Admitting a Continuous Linear Right Inverse on Ultradistributions
Let Pm be a homogeneous polynomial of degree m in n ≥ 2 variables for which the associated partial differential operator Pm(D) admits a continuous linear right inverse on C∞(Rn). Examples suggest that then for each polynomial Q of degree less than m there exists a number 0 < β < 1 such that the operator (Pm+Q)(D) admits a continuous linear right inverse on the space of all ωβ-ultradifferentiabl...
متن کاملCharacterization of projective special linear groups in dimension three by their orders and degree patterns
The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...
متن کاملRight inverses for linear, constant coefficient partial differential operators on distributions over open half spaces
Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619 – 655 (1990)] are used to prove the following: Let P 2 Cz1; . . . ; zn and denote by Pm its principal part. If P ÿ Pm is dominated by Pm then the following assertions for the partial differential operators P D and Pm D are equivalent for N 2 Snÿ1: (1) P D...
متن کاملCharacterization of $G_2(q)$, where $2 < q equiv 1(mod 3)$ by order components
In this paper we will prove that the simple group $G_2(q)$, where $2 < q equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.
متن کاملA Note on Scalar-valued Nonlinear Absolutely Summing Mappings
w,q = supφ∈BX́ ( ∑k j=1 | φ(xj) | ) 1 q . This is a natural generalization of the concept of (p; q)-summing operators and in the last years has been studied by several authors. The infimum of the L > 0 for which the inequality holds defines a norm ‖.‖as(p;q) for the case p ≥ 1 or a p-norm for the case p < 1 on the space of (p; q)-summing homogeneous polynomials. The space of all m-homogeneous (p...
متن کامل