Linear Functionals on Spaces of Measurable Functions

1998 ◽  
pp. 193-200
Author(s):  
Adriaan C. Zaanen
Keyword(s):  
Linear Functionals ◽  
Measurable Functions

scholarly journals Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Qp over Primes p

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 199 ◽  
Author(s):  
Ilwoo Cho ◽  
Palle Jorgensen
Keyword(s):  
Probability Space ◽  
Free Probability ◽  
Number Fields ◽  
Linear Functionals ◽  
Real Numbers ◽  
Probabilistic Information ◽  
Closed Intervals ◽  
Measurable Functions ◽  
Semicircular Elements

In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS .

Extension of linear functionals in Banach spaces of measurable functions

1976 ◽  
Vol 20 (5) ◽  
pp. 969-973
Author(s):  
M. S. Braverman ◽  
G. Ya. Lozanovskii
Keyword(s):  
Banach Spaces ◽  
Linear Functionals ◽  
Measurable Functions

CLASSIFICATIONS OF BOREL MEASURABLE FUNCTIONS

1994 ◽  
Vol 20 (2) ◽  
pp. 407
Author(s):  
Morayne
Keyword(s):  
Measurable Functions ◽  
Borel Measurable

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

Bounded Linear Functionals on L q

1965 ◽  
Vol 72 (7) ◽  
pp. 750
Author(s):  
W. Fulks
Keyword(s):  
Linear Functionals ◽  
Bounded Linear

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

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