Boundary Interpolation For Slice Hyperholomorphic Schur Functions,
2015
Ben Gurion University of the Negev
Boundary Interpolation For Slice Hyperholomorphic Schur Functions, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers κ1,…,κN, quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu≠1 for u=1,…,N, and quaternions s1,…,sN, we wish to find a slice hyperholomorphic Schur function s so that
limr→1r∈(0,1)s(rpu)=suforu=1,…,N,
and
limr→1r∈(0,1)1−s(rpu)su¯¯¯¯¯1−r≤κu,foru=1,…,N.
Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.
A New Resolvent Equation For The S-Functional Calculus,
2015
Chapman University
A New Resolvent Equation For The S-Functional Calculus, Daniel Alpay, Fabrizio Colombo, Jonathan Gantner, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
The S-functional calculus is a functional calculus for (n + 1)-tuples of non necessarily commuting operators that can be considered a higher dimensional version of the classical Riesz-Dunford functional calculus for a single operator. In this last calculus, the resolvent equation plays an important role in the proof of several results. Associated with the S-functional calculus there are two resolvent operators: the left S−1 L (s, T ) and the right one S−1 R (s, T ), where s = (s0, s1, . . . , sn) ∈ Rn+1 and T = (T0, T1, . . . , Tn) is …
Inner Product Spaces And Krein Spaces In The Quaternionic Setting,
2015
Chapman University
Inner Product Spaces And Krein Spaces In The Quaternionic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a closed uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters,
2015
Chapman University
Realizations Of Infinite Products, Ruelle Operators And Wavelet Filters, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the system theory notion of state-space realization of matrix-valued rational functions, we describe the Ruelle operator associated with wavelet filters. The resulting realization of infinite products of rational functions have the following four features: 1) It is defined in an infinite-dimensional complex domain. 2) Starting with a realization of a single rational matrix-function M, we show that a resulting infinite product realization obtained from M takes the form of an (infinitedimensional) Toeplitz operator with the symbol that is a reflection of the initial realization for M. 3) Starting with a subclass of rational matrix functions, including scalar-valued ones corresponding …
On Algebras Which Are Inductive Limits Of Banach Spaces,
2015
Chapman University
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding version of the well-known Wiener theorem. Finally, we consider factorization theory in these algebra, and in particular, in the associated Wiener algebra.
Wiener-Chaos Approach To Optimal Prediction,
2015
Chapman University
Wiener-Chaos Approach To Optimal Prediction, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this work we combine Wiener chaos expansion approach to study the dynamics of a stochastic system with the classical problem of the prediction of a Gaussian process based on part of its sample path. This is done by considering special bases for the Gaussian space G generated by the process, which allows us to obtain an orthogonal basis for the Fock space of G such that each basis element is either measurable or independent with respect to the given samples. This allows us to easily derive the chaos expansion of a random variable conditioned on part of the sample …
On The Indispensable Premises Of The Indispensability Argument,
2014
Institute for Advanced Studies IUSS
On The Indispensable Premises Of The Indispensability Argument, Andrea Sereni, Marco Panza
MPP Published Research
We identify four different minimal versions of the indispensability argument, falling under four different varieties: an epistemic argument for semantic realism, an epistemic argument for platonism and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed …
Metastable Behavior For Conservative Dynamics On A Finite Box With Open Boundary,
2014
Louisiana State University
Metastable Behavior For Conservative Dynamics On A Finite Box With Open Boundary, Taizo Chiyonobu, Yusuke Takagi
Communications on Stochastic Analysis
No abstract provided.
An Entropy Approach To Bose-Einstein Condensation,
2014
Louisiana State University
An Entropy Approach To Bose-Einstein Condensation, Francesco De Vecchi, Stefania Ugolini
Communications on Stochastic Analysis
No abstract provided.
Absence Of Energy Level Crossing For The Ground State Energy Of The Rabi Model,
2014
Louisiana State University
Absence Of Energy Level Crossing For The Ground State Energy Of The Rabi Model, Masao Hirokawa, Fumio Hiroshima
Communications on Stochastic Analysis
No abstract provided.
Absolute Continuity Under Time Shift For Ornstein-Uhlenbeck Type Processes With Delay Or Anticipation,
2014
Louisiana State University
Absolute Continuity Under Time Shift For Ornstein-Uhlenbeck Type Processes With Delay Or Anticipation, Jörg-Uwe Löbus
Communications on Stochastic Analysis
No abstract provided.
An Epsilon-Nash Equilibrium For Non-Linear Markov Games Of Mean-Field-Type On Finite Spaces,
2014
Louisiana State University
An Epsilon-Nash Equilibrium For Non-Linear Markov Games Of Mean-Field-Type On Finite Spaces, Rani Basna, Astrid Hilbert, Vassili N Kolokoltsov
Communications on Stochastic Analysis
No abstract provided.
Parameter Estimation From Occupation Times—A White Noise Approach,
2014
Louisiana State University
Parameter Estimation From Occupation Times—A White Noise Approach, Wolfgang Bock, Thomas Götz, Martin Grothaus, Uditha Prabhath Liyanage
Communications on Stochastic Analysis
No abstract provided.
Higher Powers Of Quantum White Noise Derivatives,
2014
Louisiana State University
Higher Powers Of Quantum White Noise Derivatives, Aymen Ettaieb, Habib Ouerdiane, Hafedh Rguigui
Communications on Stochastic Analysis
No abstract provided.
Large Deviations Estimates For Some White Noise Distributions,
2014
Louisiana State University
Large Deviations Estimates For Some White Noise Distributions, Sonia Chaari, Achref Majid, Habib Ouerdiane
Communications on Stochastic Analysis
No abstract provided.
The Structure And Properties Of Clique Graphs Of Regular Graphs,
2014
University of Southern Mississippi
The Structure And Properties Of Clique Graphs Of Regular Graphs, Jan Burmeister
Master's Theses
In the following thesis, the structure and properties of G and its clique graph clt (G) are analyzed for graphs G that are non-complete, regular with degree δ , and where every edge of G is contained in a t -clique. In a clique graph clt (G), all cliques of order t of the original graph G become the clique graph’s vertices, and the vertices of the clique graph are adjacent if and only if the corresponding cliques in the original graph have at least 1 vertex in common. This thesis mainly investigates if …
Radio Number For Fourth Power Paths,
2014
California State University - San Bernardino
Radio Number For Fourth Power Paths, Linda V. Alegria
Electronic Theses, Projects, and Dissertations
A path on n vertices, denoted by Pn, is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the order. A fourth power path, Pn4, is obtained from Pn by adding edges between any two vertices, u and v, whose distance in Pn, denoted by dPn(u,v), is less than or equal to four. The diameter of a graph G, denoted diam(G) is the greatest distance between any two distinct vertices of G. A radio labeling of a graph G is a function f that assigns to each …
A Game-Theoretic Analysis Of The Nuclear Non-Proliferation Treaty,
2014
University of Nebraska-Lincoln
A Game-Theoretic Analysis Of The Nuclear Non-Proliferation Treaty, Peter Revesz
School of Computing: Conference and Workshop Papers
Although nuclear non-proliferation is an almost universal human desire, in practice, the negotiated treaties appear unable to prevent the steady growth of the number of states that have nuclear weapons. We propose a computational model for understanding the complex issues behind nuclear arms negotiations, the motivations of various states to enter a nuclear weapons program and the ways to diffuse crisis situations.
Control Of A Finite Dam With A Lévy Input,
2014
Louisiana State University
Control Of A Finite Dam With A Lévy Input, Mohamed Abdel-Hameed
Communications on Stochastic Analysis
No abstract provided.
Powers Of An Infinite Dimensional Brownian Motion Associated With The Product Of Distributions,
2014
Louisiana State University
Powers Of An Infinite Dimensional Brownian Motion Associated With The Product Of Distributions, Kimiaki Saitô, Takashi Shimada
Communications on Stochastic Analysis
No abstract provided.
