Open Advanced Search

Log in
Enterprise Plans
Sign Up

Log in
Sign Up
Enterprise Plans
Browse
Features
Pricing

DeepDyve

Advanced Search

show/hide query preview

With all of the words or DOIs:

DeepDyve's default query mode: search by keyword or DOI.

With the exact phrase:

Require these words, in this exact order. Do not surround your terms in double-quotes ("") in this field.

With at least one of the words:

Find any of these words, separated by spaces

Without the words:

Exclude each of these words, separated by spaces

With words in the article title:

Search for these terms only in the title of an article

Published between the years:

With the following authors:

Most effective as: LastName, First Name or Lastname, FN

With words in the journal name:

Search for articles published in journals where these words are in the journal name

Reset filters

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue.

Slice Hyperholomorphic Schur Analysis

Part of the Operator Theory: Advances and Applications Book Series (volume 256)

DOI: 10.1007/978-3-319-42514-6

ISBN: 978-3-319-42513-9

Publisher: Springer International Publishing - Springer Journals

Dec 11, 2016

1 - 10 of 11 Chapters

LitStream

Preliminaries

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 3 –21

[In this chapter we present some definitions and results which play an important role in Schur analysis. In particular, we discuss indefinite inner product spaces, reproducing kernel spaces, and two extension problems.]
LitStream

Rational Functions

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 23 –35

[Since this book is intended to (at least) two different audiences, we recall in the present chapter the main features of realization theory for matrix-valued rational functions (that is, of matrices whose entries are quotients of polynomials). Note that realizations of elements in certain...
LitStream

Schur Analysis

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 37 –47

[As discussed in Chapter 1, functions analytic and contractive in the open unit disk, the Schur functions, are part of classical mathematics, as is illustrated by the works of Schur [261, 262], Takagi [270, 271], and Bloch [98], to name a few. They play an important role in numerous areas of...
LitStream

Finite-dimensional Preliminaries

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 51 –69

[In this chapter we discuss the finite-dimensional aspects of quaternionic analysis which are needed in the sequel. In the first section we survey the main properties of quaternions. Then we consider quaternionic polynomials and we discuss their zeros. In the third section we discuss quaternionic...
LitStream

Quaternionic Functional Analysis

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 71 –115

[To develop Schur analysis in the slice hyperholomophic setting, a number of facts and results from quaternionic functional analysis for which no references were available are needed. These are developed in the present chapter, largely taken from [35]. Most of the results can be proved with the...
LitStream

Slice Hyperholomorphic Functions

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 117 –164

[In the first section of this chapter we give a brief survey of the theory of slice hyperholomorphic functions, and we provide the basic results needed in the sequel. The theory is much more developed and we refer the reader to the Introduction to Part II of the present work for references. Then,...
LitStream

Operator-valued Slice Hyperholomorphic Functions

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 165 –194

[In this chapter we introduce slice hyperholomorphic functions with values in a quaternionic Banach space. As in the complex case, there are two equivalent notions, namely weak and strong slice hyperholomorphicity. In order to properly define a multiplication between slice hyperholomorphic...
LitStream

Reproducing Kernel Spaces and Realizations

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 197 –240

[The tools developed in the previous chapters allow us to define and study in the operator-valued case the various families of functions appearing in classical Schur analysis. In this section we obtain realization formulas for these functions. These formulas in turn have important consequences,...
LitStream

Rational Slice Hyperholomorphic Functions

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 241 –264

[Rational functions play an important role in linear system theory, and in the noncommutative case we mention in particular the works [225, 264, 265]. We also mention [65], which is set in the framework of noncommutative probability. There the approach uses a topological algebra of a very special...
LitStream

First Applications: Scalar Interpolation and First-order Discrete Systems

Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene

Pages: 265 –307

[In the present chapter we discuss the Schur algorithm and some interpolation problems in the scalar case.We make use, in particular, of the theory of J-unitary rational functions presented in Chapter 9. We also discuss first-order discrete systems. In the classical case, interpolation problems...

results per page

Browse All eBooks

Features

Search and discover articles on DeepDyve, PubMed, and Google Scholar
Read the full-text of open access and premium content
Organize articles with folders and bookmarks
Collaborate on and share articles and folders

Info

Pricing
Enterprise Plans
Browse Journals & Topics
About DeepDyve

Help

Help
Publishers
Contact Us

Sign up for your DeepDyve account now!

Read and print from thousands of top scholarly journals.

System error. Please try again!

Continue with Facebook

By signing up, you agree to DeepDyve’s Terms of Service and Privacy Policy.

Already have an account? Log in

Save Article to Bookmarks

Bookmark this article. You can see your Bookmarks on your DeepDyve Library.

To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.

Subscribe to Journal Email Alerts

To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Follow a Journal

To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.

Our policy towards the use of cookies

All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.

cookie policy