Related papers: Notes of functional analysis
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
This text is meant for analysis students who want to learn more about the effects of the axiom of choice on functional analysis, and the things that may go wrong in its absence. As this is a text aimed for analysis students, we will not…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A new edition of Walter K. Hayman's 'Research Problems in Function Theory' (1967), containing over five hundred function theory and complex analysis problems, along with all progress updates over the last 51 years. The final publication…
Just a survey on I0: The basics, some things known but never published, some things published but not known.
Methods were initiated by Mark Kac and Richard Feynman to evaluate random functionals of the form $\int^t_0V(X_s)ds$ for a nonnegative $V$ and a Markov process $X_t$. Their results evolved into the well known Feynman Kac formula.…
While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…
A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.
In the 49th International Symposium on Functional Equations, J. Acz\'el asked for the monotonic solutions of a certain one-parameter family of functional equations. In this short note we find that for a certain value of the parameter the…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
These are lecture notes for the AGRA II school, which took place in August 2015 at Universidad de San Antonio Abad del Cusco (Per\'u). They are geared towards graduate students and young researchers. I. Modular forms and Shimura curves (R.…
Quantum theory and functional analysis were created and put into essentially their final form during similar periods ending around 1930. Each was also a key outcome of the major revolutions that both physics and mathematics as a whole…
These are the notes from my courses on the arithmetic of quadratic forms.
This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set.…
The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…