scholarly journals Paley–Wiener properties for spaces of entire functions

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
Elmira Nabizadeh ◽  
Christine Pfeuffer ◽  
Joachim Toft
Keyword(s):  
Function Space ◽  
Entire Functions ◽  
Test Function ◽  
Test Function Space

Abstract We deduce Paley–Wiener results in the Bargmann setting. At the same time we deduce characterisations of Pilipović spaces of low orders. In particular we improve the characterisation of the Gröchenig test function space $$\mathcal {H}_{\flat _1}=\mathcal {S}_C$$ H ♭ 1 = S C , deduced in Toft (J Pseudo-Differ Oper Appl 8:83–139, 2017).

Continuous wavelet transform involving canonical convolution

2019 ◽  
Vol 13 (06) ◽  
pp. 2050104
Author(s):  
Zamir Ahmad Ansari
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Convolution Operator ◽  
Linear Canonical Transform ◽  
Continuous Wavelet ◽  
Test Function ◽  
Test Function Space

The main objective of this paper is to study the continuous wavelet transform in terms of canonical convolution and its adjoint. A relation between the canonical convolution operator and inverse linear canonical transform is established. The continuity of continuous wavelet transform on test function space is discussed.

scholarly journals Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Byung Keun Sohn
Keyword(s):  
Function Space ◽  
Dual Space ◽  
Ultradifferentiable Functions ◽  
Tempered Distributions ◽  
Test Function ◽  
Test Function Space

Let Sω′(R) be the space of tempered distributions of Beurling type with test function space Sω(R) and let Eω,p be the space of ultradifferentiable functions with arbitrary support having a period p. We show that Eω,p is generated by Sω(R). Also, we show that the mapping Sω(R)→Eω,p is linear, onto, and continuous and the mapping Sω,p′(R)→Eω,p′ is linear and onto where Sω,p′(R) is the subspace of Sω′(R) having a period p and Eω,p′ is the dual space of Eω,p.

scholarly journals Test function space for Wick power series

2000 ◽  
Vol 123 (3) ◽  
pp. 709-725 ◽  
Author(s):  
A. G. Smirnov ◽  
M. A. Solov'ev
Keyword(s):  
Power Series ◽  
Function Space ◽  
Test Function ◽  
Test Function Space

The n-Dimensional Distributional Hankel Transformation

1975 ◽  
Vol 27 (2) ◽  
pp. 423-433 ◽  
Author(s):  
E. L. Koh
Keyword(s):  
Function Space ◽  
Generalized Functions ◽  
One Dimension ◽  
Dimensional Case ◽  
Hankel Transformation ◽  
Test Function ◽  
Test Function Space

The Hankel transformation was extended to certain generalized functions of one dimension [1; 2; 3]. In this paper, we develop the n-dimensional case corresponding to [1]. The procedure in [1] is briefly as follows:A test function space Hμ is constructed on which the μth order Hankel transformation hμ defined byis an automorphism whenever μ ≧ —1/2. The generalized transformation hμ' is then defined on the dual Hμ' as the adjoint of hμ through a Parseval relation, i.e.

On the Bogolyubov endomorphisms of the renormalized square of white noise algebra

2021 ◽  
Author(s):  
Habib Rebei ◽  
Slaheddine Wannes
Keyword(s):  
White Noise ◽  
Function Space ◽  
The Other ◽  
Linear Transformations ◽  
Test Function ◽  
Canonical Commutation Relations ◽  
Arbitrary Complex ◽  
Borel Functions ◽  
Test Function Space ◽  
Complex Valued

We introduce the quadratic analogue of the Bogolyubov endomorphisms of the canonical commutation relations (CCR) associated with the re-normalized square of white noise algebra (RSWN-algebra). We focus on the structure of a subclass of these endomorphisms: each of them is uniquely determined by a quadruple [Formula: see text], where [Formula: see text] are linear transformations from a test-function space [Formula: see text] into itself, while [Formula: see text] is anti-linear on [Formula: see text] and [Formula: see text] is real. Precisely, we prove that [Formula: see text] and [Formula: see text] are uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text], into itself. Under some additional analytic conditions on [Formula: see text] and [Formula: see text], we discover that we have only two equivalent classes of Bogolyubov endomorphisms, one of them corresponds to the case [Formula: see text] and the other corresponds to the case [Formula: see text]. Finally, we close the paper by building some examples in one and multi-dimensional cases.

Representation of Symmetries and Observables in Functional Hilbert Space. II.

1972 ◽  
Vol 27 (1) ◽  
pp. 7-22 ◽  
Author(s):  
A. Rieckers
Keyword(s):  
Hilbert Space ◽  
Relativistic Quantum ◽  
Preceding Paper ◽  
Complex Hilbert Space ◽  
Unbounded Operators ◽  
Test Function ◽  
Test Function Space ◽  
Quantum Observables ◽  
Set Up ◽  
Real Test

Abstract The representation of infinitesimal generators corresponding to the group representation dis-cussed in the preceding paper is analyzed in the Hilbert space of functionals over real test functions. Explicit expressions for these unbounded operators are constructed by means of the functio-nal derivative and by canonical operator pairs on dense domains. The behaviour under certain basis transformations is investigated, also for non-Hermitian generators. For the Hermitian ones a common, dense domain is set up where they are essentially selfadjoint. After having established a one-to-one correspondence between the real test function space and a complex Hilbert space the theory of quantum observables is applied to the functional version of a relativistic quantum field theory.

scholarly journals The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Function Space ◽  
Variable Exponent ◽  
Entire Functions ◽  
Shift Operator ◽  
Complex Variables ◽  
Power Series Space ◽  
Series Space ◽  
Backward Shift ◽  
Type Variable ◽  
Formal Power

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

Pengujian pada Aplikasi Penggajian Pegawai dengan menggunakan Metode Blackbox

2020 ◽  
Vol 5 (1) ◽  
pp. 61
Author(s):  
Vadlan Febrian ◽  
Muhamad Rizki Ramadhan ◽  
Muhammad Faisal ◽  
Aries Saifudin
Keyword(s):  
Data Entry ◽  
Black Box ◽  
Application Form ◽  
Value Analysis ◽  
Test Function ◽  
Testing Method ◽  
Black Box Testing ◽  
Sample Testing ◽  
Testing Techniques ◽  
Program Error

In this employee payroll application, if there is an error program there will be a loss for employees and the company. Losses for employees, if this application program error occurs then the salary reduction will experience delays due to the difficulty in the process of calculating employee salaries and employees will be late in receiving salaries. Losses for the company, if there is an error program in this application, the company will suffer losses if the employee wants a salary reduction quickly but the company cannot calculate quickly and accurately. In solving this problem, the authors use the black box testing method. Black box testing method is a test that sees the results of execution through test data and ensures the function of the software. Black box testing method has several testing techniques, namely Sample Testing, Boundary Value Analysis, Equivalence Partitions and others. From the testing techniques that have been mentioned, we use the Equivalence Partitions testing technique. Equivalence Partitions are tests that refer to data entry on the employee payroll application form, input will be tested and then put together based on the test function, both valid and invalid values. The expected results of this test are a payroll system for employees who are computerized, have standard rules in the process of developing the program so that it is easy to develop and maintain, and can minimize errors in processing salary calculations for employees.

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