The injection and the projection theorem for spectral sets

1981 ◽  
Vol 92 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Wilfried Hauenschild ◽  
Jean Ludwig
Keyword(s):  
Spectral Sets ◽  
Projection Theorem

The projection theorem for spectral sets

1986 ◽  
Vol 101 (1) ◽  
pp. 1-10
Author(s):  
Mohammed El Bachir Bekka
Keyword(s):  
Spectral Sets ◽  
Projection Theorem

Decomposing numerical ranges along with spectral sets

2009 ◽  
Vol 57 (5) ◽  
pp. 431-437
Author(s):  
Franciszek Hugon Szafraniec
Keyword(s):  
Spectral Sets

scholarly journals Partial inverse problems for Sturm–Liouville operators on trees

2017 ◽  
Vol 147 (5) ◽  
pp. 917-933 ◽  
Author(s):  
Natalia Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Sets ◽  
Spectral Problems ◽  
Partial Inverse ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, inverse spectral problems for Sturm–Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b – 1 spectral sets uniquely determine the potential functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

The Quasi-Isomorphism Theorem

2019 ◽  
pp. 185-194
Author(s):  
Richard Evan Schwartz
Keyword(s):  
Affine Transformation ◽  
Equivalence Theorem ◽  
Isomorphism Theorem ◽  
Orbit Equivalence ◽  
Geometric Properties ◽  
Projection Theorem ◽  
Canonical Bijection ◽  
Arithmetic Graph

This chapter proves the Quasi-Isomorphism Theorem modulo two technical lemmas, which will be dealt with in the next two chapters. Section 18.2 introduces the affine transformation TA from the Quasi-Isomorphism Theorem. Section 18.3 defines the graph grid GA = TA(Z2) and states the Grid Geometry Lemma, a result about the basic geometric properties of GA. Section 18.4 introduces the set Z* that appears in the Renormalization Theorem and states the main result about it, the Intertwining Lemma. Section 18.5 explains how the Orbit Equivalence Theorem sets up a canonical bijection between the nontrivial orbits of the plaid PET and the orbits of the graph PET. Section 18.6 reinterprets the orbit correspondence in terms of the plaid polygons and the arithmetic graph polygons. Everything is then put together to complete the proof of the Quasi-Isomorphism Theorem. Section 18.7 deduces the Projection Theorem (Theorem 0.2) from the Quasi-Isomorphism Theorem.

scholarly journals On a conjecture about spectral sets

2004 ◽  
Vol 139 (1-3) ◽  
pp. 1-15
Author(s):  
Karim Belaid ◽  
Othman Echi
Keyword(s):  
Spectral Sets

Orthogonal projection theorem

1998 ◽  
pp. 135-139
Author(s):  
Richard Tolimieri ◽  
Myoung An
Keyword(s):  
Orthogonal Projection ◽  
Projection Theorem
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