The transforms generated by a real linear regular self-adjoint boundary value problem of fourth order. (Q2782454)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The transforms generated by a real linear regular self-adjoint boundary value problem of fourth order. |
scientific article; zbMATH DE number 1724386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The transforms generated by a real linear regular self-adjoint boundary value problem of fourth order. |
scientific article; zbMATH DE number 1724386 |
Statements
19 August 2003
0 references
integal transform
0 references
\(L_2\)-space
0 references
linear differential equation
0 references
linear boundary value problem
0 references
range
0 references
0.86137533
0 references
0.8454966
0 references
0.84371614
0 references
0.84036976
0 references
0.8369535
0 references
0.83478487
0 references
The transforms generated by a real linear regular self-adjoint boundary value problem of fourth order. (English)
0 references
The present paper deals with the integral transform NEWLINE\[NEWLINETf(u)=\int^{\infty}_{0}f(x)\phi(x,u)\,dxNEWLINE\]NEWLINE the kernel \(\phi(x,u)\) of which is expressed in terms of solutions of a linear initial boundary value problem for a fourth-order linear homogeneous ordinary differential equation. Mapping properties of the operator \(T\) are studied. In particular, it is proved that the range \(T(L_2(0,\infty))\) of this transform is a Hilbert space with a suitable inner product.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00021].
0 references
