Concerning Exponential Bases on Multi-Rectangles of ℝ d $$\boldsymbol {\mathbb {R}^d}$$

2019 ◽  
pp. 65-85
Author(s):  
Laura De Carli
Keyword(s):  
Exponential Bases

scholarly journals A simple construction of exponential bases in L2 of the union of several intervals

1995 ◽  
Vol 38 (1) ◽  
pp. 171-177 ◽  
Author(s):  
Kristian Seip
Keyword(s):  
Riesz Basis ◽  
Partial Result ◽  
Simple Construction ◽  
Real Numbers ◽  
Exponential Bases ◽  
Several Intervals

It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.

Interpolation of Subspaces and Applications to Exponential Bases

2015 ◽  
pp. 509-532
Author(s):  
Fritz Gesztesy ◽  
Gilles Godefroy ◽  
Loukas Grafakos ◽  
Igor Verbitsky
Keyword(s):  
Exponential Bases

scholarly journals Frame Spectral Pairs and Exponential Bases

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Christina Frederick ◽  
Azita Mayeli
Keyword(s):  
Spectral Pairs ◽  
Exponential Bases

Exponential bases in L2

1971 ◽  
Vol 5 (1) ◽  
pp. 31-38 ◽  
Author(s):  
V. �. Katsnel'son
Keyword(s):  
Exponential Bases

scholarly journals On unconditional exponential bases in weighted spaces on real axis

2015 ◽  
Vol 7 (3) ◽  
pp. 108-118
Author(s):  
Artur Airatovich Yunusov
Keyword(s):  
Real Axis ◽  
Weighted Spaces ◽  
Exponential Bases

Exponential Bases in Sobolev Spaces in Control and Observation Problems

1999 ◽  
pp. 33-42
Author(s):  
Sergei A. Avdonin ◽  
Sergei A. Ivanov ◽  
David L. Russell
Keyword(s):  
Sobolev Spaces ◽  
Exponential Bases

Exponential bases in Sobolev spaces in control and observation problems for the wave equation

2000 ◽  
Vol 130 (5) ◽  
pp. 947-970 ◽  
Author(s):  
S. A. Avdonin ◽  
S. A. Ivanov ◽  
D. L. Russell
Keyword(s):  
State Space ◽  
Control Systems ◽  
Sobolev Spaces ◽  
Fourier Method ◽  
Exponential Families ◽  
Control Space ◽  
Space State ◽  
Exponential Bases ◽  
And Control ◽  
Control Operators

The Fourier method in control systems reduces the study of controllability/observability to the study of related exponential families. In this paper we present examples of such systems, specifically those for which we can prove that the related exponential families form a Riesz basis in corresponding appropriately defined Sobolev spaces. This makes it possible to choose ‘natural’ pairs of spaces: the state space observability space and the control space state space, depending on whether an observation or a control problem is studied, respectively, so that the observation and control operators are isomorphisms.

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