# Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces

## Abstract

In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigation of the problem.

- Authors:

- Irkutsk State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771267

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; 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; BANACH SPACE; CAUCHY PROBLEM; FUNCTIONS; INTEGRALS; INTEGRO-DIFFERENTIAL EQUATIONS; KERNELS; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Falaleev, M. V., E-mail: mvfalaleev@gmail.com.
```*Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3789-X.

```
Falaleev, M. V., E-mail: mvfalaleev@gmail.com.
```*Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces*. United States. doi:10.1007/S10958-018-3789-X.

```
Falaleev, M. V., E-mail: mvfalaleev@gmail.com. Tue .
"Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces". United States. doi:10.1007/S10958-018-3789-X.
```

```
@article{osti_22771267,
```

title = {Fundamental Operator-Valued Functions of Singular Integrodifferential Operators in Banach Spaces},

author = {Falaleev, M. V., E-mail: mvfalaleev@gmail.com},

abstractNote = {In this paper, using methods of the theory of generalized functions in Banach spaces, we examine the Cauchy problem for an abstract integrodifferential equation of a specific type. Under the assumption that there exist the complete Jordan structure of the differential part of the equation and the order of the zero of the kernel of the integral part, the fundamental operator-valued function (the fundamental solution) is constructed for the corresponding integrodifferential operator, which is used for further investigation of the problem.},

doi = {10.1007/S10958-018-3789-X},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.