Article
Mathematics
Dariusz Kosz, Javier C. Martinez-Perales, Victoria Paternostro, Ezequiel Rela, Luz Roncal
Summary: This study investigates maximal operators associated with bases on the infinite-dimensional torus T-omega and explores their weak-type properties. It has been found that the maximal operator corresponding to the dyadic basis is of weak type (1,1), while the operator associated with the natural general basis is not. The study also examines the behavior of maximal functions for a wide class of intermediate bases and investigates the properties of weighted maximal operators in the Muckenhoupt and reverse Holder classes.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics
Jingbo Xia
Summary: The paper proved an exact integral formula for the Schatten p-norm of Hankel operators on the one-variable Hardy space for p = 2, 4, and 6. It was also shown that these are the only values of p for which such a formula is possible. Furthermore, it was pointed out that the only meaningful multi-variable analogue of this formula is when n = 2 and p = 6.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics
Zhicheng Zeng, Xiaofeng Wang, Zhangjian Hu
Summary: This paper characterizes Schatten p-class Hankel operators with general symbols acting on Bergman spaces with exponential weights when 0 < p < infinity.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics
Zhangjian Hu, Jani A. Virtanen
Summary: This paper provides a complete characterization of Schatten class Hankel operators H-f acting on weighted Segal-Bargmann spaces F-2(phi) using the notion of integral distance to analytic functions in C-n and Hörmander's partial derivative-theory. Based on our characterization, for f ∈ L-infinity and 1 < p < infinity, we prove that H-f is in the Schatten class S-p if and only if H ((f) over bar) ∈ S-p,S-, which was previously known only for the Hilbert-Schmidt class S-2 of the standard Segal-Bargmann space F-2(phi) with phi(z) = alpha vertical bar z vertical bar(2).
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics
Zhamgjian Hu, Jani A. Virtanen
Summary: The authors present a valid proof of Theorem 1.2 and rectify the statement of Theorem 2.6 in their paper published in Trans. Amer. Math. Soc. 375 (2022), 3733-3753.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Quantum Science & Technology
Martina Gschwendtner, Andreas Winter
Summary: This research extends the concept of finite-dimensional programmable quantum processors to infinite dimension, providing upper and lower bounds for the program dimension needed to implement energy-limited quantum channels successfully. It specifically focuses on the implementation of Gaussian channels, including gauge-covariant Gaussian channels, and provides bounds on the program dimension required for implementing all Gaussian unitary channels. These bounds are derived from a direct information-theoretic argument based on a generalization from finite to infinite dimension of a certain lemma for unitaries.
Article
Automation & Control Systems
Salvatore Federico, Giorgio Ferrari, Frank Riedel, Michael Roeckner
Summary: This study presents a rigorous formulation of a class of infinite-dimensional singular stochastic control problems and derives necessary and sufficient first-order conditions for optimality. The optimal control is determined in a model by exploiting these conditions, using techniques such as semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematics
S. D. Glyzin, A. Yu. Kolesov
Summary: This paper examines a special class of diffeomorphisms on the infinite-dimensional torus, presenting elements of hyperbolic theory with definitions, auxiliary facts, and advanced results.
RUSSIAN MATHEMATICAL SURVEYS
(2022)
Article
Mathematics, Applied
Shivansh Pandey, Brundaban Sahu
Summary: This study presents a set of kernel functions for studying the Jacobi group and focuses on the nonvanishing of 2m Dirichlet series associated with Jacobi forms, as well as Poincare series.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Physics, Mathematical
Sergio Albeverio, Toshinao Kagawa, Yumi Yahagi, Minoru W. Yoshida
Summary: This article presents general theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces, as well as an existence theorem for Hunt processes associated with Dirichlet forms. These theorems are applied to the problem of stochastic quantizations of Euclidean Φ(4)(d) fields for d = 2, 3.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Dhairya Shah, Manoj Sahni, Ritu Sahni, Ernesto Leon-Castro, Maricruz Olazabal-Lugo
Summary: In this second part of a series of papers, we extend the theorems discussed in the first part to infinite series. We then use these theorems to derive new results involving different mathematical functions. We also investigate the behavior of these newly developed functions and provide examples showcasing the broad scope and potential of the theorems in creating a new field under the realm of number theory and analysis.
Article
Mathematics, Applied
Alexey Kuznetsov
Summary: In this work, an analogue of the Lagrange Inversion Theorem for Dirichlet series is proven. The proof relies on studying properties of Dirichlet convolution polynomials, which are analogous to convolution polynomials introduced by Knuth.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Xiaofeng Wang, Jin Xia, Youqi Liu
Summary: This paper studies Toeplitz and Hankel operators on exponential weighted Bergman spaces, and obtains sufficient and necessary conditions for them to belong to the Schatten-p class using averaging functions of symbols. The Schatten-h class Toeplitz and Hankel operators are also characterized for a continuous increasing convex function h.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2023)
Article
Operations Research & Management Science
Hasan Yilmaz
Summary: We present a generalization of multiplier rules for infinite-dimensional optimization problems with a finite number of constraints, where the assumptions on the differentiability of the functions are weaker compared to existing results.
Article
Mathematics
Sergio Albeverio, Toshinao Kagawa, Shuji Kawasaki, Yumi Yahagi, Minoru W. Yoshida
Summary: The general framework of non-local Markovian symmetric forms on weighted l(p) spaces is applied to various probability measure spaces, and the corresponding Markov processes for non-local stochastic quantization are constructed.
POTENTIAL ANALYSIS
(2022)
Article
Mathematics
Ole Fredrik Brevig, Karl-Mikael Perfekt, Kristian Seip
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2019)
Article
Mathematics, Applied
Johan Helsing, Karl-Mikael Perfekt
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
Article
Mathematics
Frederic Bayart, Ole Fredrik Brevig, Antti Haimi, Joaquim Ortega-Cerda, Karl-Mikael Perfekt
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics, Applied
Karl-Mikael Perfekt
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2019)
Article
Mathematics, Applied
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt
ANALYSIS AND MATHEMATICAL PHYSICS
(2019)
Article
Mathematics
Ole Fredrik Brevig, Karl-Mikael Perfekt
JOURNAL OF FUNCTIONAL ANALYSIS
(2020)
Article
Mathematics, Applied
Luigi D'Onofrio, Luigi Greco, Karl-Mikael Perfekt, Carlo Sbordone, Roberta Schiattarella
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2020)
Article
Mathematics, Applied
Karl-Mikael Perfekt
Summary: The study considers the plasmonic eigenvalue problem for a general 2D domain with a curvilinear corner, proving a limiting absorption principle applicable near the essential spectrum. It is shown that the corner generates absolutely continuous spectrum with multiplicity 1 and discrete embedded eigenvalues, without any singular continuous spectrum.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2021)
Article
Mathematics
Karl-Mikael Perfekt
Summary: This study focuses on the class of multiple Fourier series associated with functions in the Dirichlet space of the polydisc, proving that each series can be summed with unrestricted rectangular partial sums, with exceptions occurring only on sets of zero multi-parametric logarithmic capacity. Additionally, it is shown that the multi-parametric logarithmic capacity characterizes exceptional sets for radial variation and radial limits of Dirichlet space functions, with results extending to the vector-valued setting.
POTENTIAL ANALYSIS
(2021)
Article
Mathematics
Ole Fredrik Brevig, Karl-Mikael Perfekt
Summary: This paper introduces a mean counting function for Dirichlet series, which is analogous to the Nevanlinna counting function in the function theory of Hardy spaces. The existence of the mean counting function is linked to Jessen and Tornehave's resolution of the Lagrange mean motion problem. The mean counting function is used to characterize all compact composition operators with Dirichlet series symbols on the Hardy-Hilbert space of Dirichlet series.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Anne-Sophie Bonnet-Ben Dhia, Simon N. Chandler-Wilde, Sonia Fliss, Christophe Hazard, Karl-Mikael Perfekt, Yohanes Tjandrawidjaja
Summary: In this paper, a new formulation for the half-space matching (HSM) method is proposed, combining it with complex-scaling technique, which is provably well-posed for real wavenumbers and has computational attractiveness. The effectiveness of the method is validated by studying double-layer potential integral operators on intersecting infinite lines and their analytic continuations.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Wei Li, Karl-Mikael Perfekt, Stephen P. Shipman
Summary: This article constructs a surface with a special essential spectrum structure, where the eigenvalues of different Fourier components are embedded within each other, resulting in infinitely many eigenvalues for the entire operator. The proof requires certain conditions on the perturbation and singularity.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics
Ole Fredrik Brevig, Karl-Mikael Perfekt
Summary: This paper studies composition operators generated by specific symbols on Hilbert spaces and estimates their approximation numbers under certain conditions. It also addresses the orthogonal decomposition problem of Dirichlet series consisting of a subset of prime numbers P. In addition, it explores the case where the symbol is supported on a single prime number and describes the compactness of operators in terms of the ordinary Nevanlinna counting function.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics
Ole Fredrik Brevig, Karl-Mikael Perfekt
Summary: This paper introduces a bounded Hankel operator problem in the Paley-Wiener space, which does not arise from a bounded symbol.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Karl-Mikael Perfekt
NEW YORK JOURNAL OF MATHEMATICS
(2019)
