# Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator

## Abstract

We consider the action of the quadratic form of the Laplace operator and its extensions in subspaces of linear combinations of the “transverse” and “longitudinal” functions with the fixed orbital momentum with respect to the coordinate origin. In the statement of the problem, it is required that the extensions obtained, after the transfer back to the space of vector functions, can be represented as simple limit expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace. Bibliography: 5 titles.

- Authors:

- St.Petersburg Department of the Steklov Mathematical Institute (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771468

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 229; Journal Issue: 5; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; LAPLACIAN; MATHEMATICAL SPACE; ORBITAL ANGULAR MOMENTUM; VECTORS

### Citation Formats

```
Bolokhov, T. A., E-mail: timur@pdmi.ras.ru.
```*Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3691-6.

```
Bolokhov, T. A., E-mail: timur@pdmi.ras.ru.
```*Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator*. United States. doi:10.1007/S10958-018-3691-6.

```
Bolokhov, T. A., E-mail: timur@pdmi.ras.ru. Thu .
"Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator". United States. doi:10.1007/S10958-018-3691-6.
```

```
@article{osti_22771468,
```

title = {Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator},

author = {Bolokhov, T. A., E-mail: timur@pdmi.ras.ru},

abstractNote = {We consider the action of the quadratic form of the Laplace operator and its extensions in subspaces of linear combinations of the “transverse” and “longitudinal” functions with the fixed orbital momentum with respect to the coordinate origin. In the statement of the problem, it is required that the extensions obtained, after the transfer back to the space of vector functions, can be represented as simple limit expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace. Bibliography: 5 titles.},

doi = {10.1007/S10958-018-3691-6},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 229,

place = {United States},

year = {2018},

month = {3}

}

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