Request Explain underlined portion from "Functional Analysis" by BV Limaye 22.6 LemmaLet {a} be an orthonormal set in an inner product space X andTEX. LetEz = {ua (t, ua) #0}.Then E is a countable set, say E₂ = {₁, 2,...}, and ((x, un)) { l².If E, is denumerable, then (x, un) → 0 as n-→∞.Further, if X is a Hilbert space, then Σn (x, un)un converges inX to some y such that (z-y) ua, that is, (2, ua) (y, ua) forevery a.Proof:If x = 0, there is nothing to prove. Let x 0. For j = 1,2,..., letEj = {ua |||| ≤j|(t, ua)|}.Fix j. Suppose that E, contains distinct elements Uaam. Thenmj0

Given that 0<mjx2≤j2∑n=1mjx,uαn2. The objective is to explain the statement.

Answered: mj 0 | bartleby

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Explain a General Approach to Modeling Nonlinearities Using Multiple Regression?
Differentiate phenomenological from mechanistic modeling.
RequiredPage 92 The company uses the number of professional hours as the cost driver for office support costs. Use an algebraic equation to describe how total office support costs can be estimated. Use a spreadsheet program to perform a regression analysis. Use office support costs as the dependent variable (Y) and the professional hours as the independent variable (X). Determine the total fixed cost per office and variable cost per professional hour. Identify the R2 statistic provided by the Excel program and explain what it means. Mr. Dean plans to open a new branch office in a Dallas suburb. He expects that the monthly professional hours will be 3,000. Estimate the total office support cost for Mr. Dean. What portion of the total cost is fixed and what portion is variable? Explain how multiple regression analysis could be used to improve the accuracy of the cost estimates. *You will use excel to setup a worksheet with your data and run regression analysis.*
Define Method of Variation of Parameters ?
differntiate question 3,4 and 5
distinguish between the unit of analysis and the aggregates?
Assignment: Analyze Filling Line Problems Using Control Charting Attached Files: File Filling line example for X-bar & control chart.xlsxOpen this document with ReadSpeaker docReader (13.354 KB) Using the provided data, calculate the control limits (X-bar and r-chart, Capability Index, create a control chart, and calculate the percentage of units that are expected to be out of spec (z-value). Show your work A quick way to do the percents part of the filling line problem (you know, the percent underfilled, the percent overfilled, etc.), is to use Excel's norm.dist function rather than looking it up on a printed Z table. Use the norm.dist excel function with the LSL in the first position in the parameter list. Norm.dist gives you the left side return from the Z table. "Excel offers you the NORM.DIST statistical function for working with normal distributions. The NORM.DIST function calculates the probability that variable X falls below or at a specified value"…
Explain Conducting Qualitative Field Research?
This activity demonstrates how to create graphics to enhance the presentation of quantitative data Scenario The sales manager for a small manufacturer is interested in marketing the company's rain coat line in a new area of the country. As a first step to establishing a marketing plan she has asked you to produce some graphs showing the market share of the products sold over the past several years in the region. Analysis After some research, you acquire the approximate sales for each of the competing products presently in the region under consideration (See the data given below). The question now is to show how best to organize the data to take advantage of a graphical analysis. Pie charts give a quick overview of the market share "slices” each competitor presently enjoys. So you decide to use a pie chart to graph the most recent year's sales data for the region. This will give a good indication of just who the market leaders are and how crowded it is at the top. Next, you decide to…

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS