When working with dates, it is advisable to use a dedicated library for date handling to minimize errors in your code.

MomentJS is highly recommended.

const currentDate = moment();
const inputDate = moment("2016-04-17T11:45:00Z");
const isCurrentWeek = (currentDate.isoWeek() === inputDate.isoWeek())

Note: It's important to mention that starting from 2020, MomentJS may not be the best choice for new projects

This function appears to be operational for me.

function checkIfDateIsInCurrentWeek(date) {
  const currentDateObj = new Date();
  const currentDate = currentDateObj.getDate();
  const currentDay = currentDateObj.getDay();

  // get the first date of the week
  const firstDayOfWeek = new Date(currentDateObj.setDate(currentDate - currentDay));

  // get the last date of the week
  const lastDayOfWeek = new Date(firstDayOfWeek);
  lastDayOfWeek.setDate(lastDayOfWeek.getDate() + 6);

  // check if the date falls within the current week
  return date >= firstDayOfWeek && date <= lastDayOfWeek;
}

const specificDate = new Date();
const isWithinCurrentWeek = checkIfDateIsInCurrentWeek(specificDate);

<div ng-app="myApp">
<div class="container" ng-controller="Ctrl_List">

    <h1>{{currentDate}}</h1>
    <h1>{{numberCurrentDateWeeks}}</h1>

    <h1>{{yourDate}}</h1>
    <h1>{{numberYourDateWeeks}}</h1>

 </div>
</div>

......

angular.module('myApp', [])
.controller("Ctrl_List", ["$scope", "$filter", function(s, $filter) {
  s.yourDate = '2016-04-23T11:45:00Z'
  s.currentDate = new Date();

  s.numberCurrentDateWeeks = $filter('date')(s.currentDate, "w");
  s.numberYourDateWeeks = $filter('date')(s.yourDate, "w");

}]);

you can now access the Week numbers to compare or do any other operations as needed

cheers !

Although not the most efficient solution, I believe this code is highly legible:

function checkIfInCurrentWeek (inputDate) {
  const currentDate = new Date();

  const currentDayOfWeek = (currentDate.getDay() + 6) % 7; // Ensuring Sunday is represented as 6 instead of 0
  const currentDayOfMonth = currentDate.getDate();
  const mondayOfCurrentWeek = currentDayOfMonth - currentDayOfWeek;

  const startOfCurrentWeek = new Date(+currentDate);
  startOfCurrentWeek.setDate(mondayOfCurrentWeek);
  startOfCurrentWeek.setHours(0, 0, 0, 0);

  const startOfNextWeek = new Date(+startOfCurrentWeek);
  startOfNextWeek.setDate(mondayOfCurrentWeek + 7);

  return inputDate >= startOfCurrentWeek && inputDate < startOfNextWeek;
}

To determine if a date falls within the current week, you can utilize a simple function without relying on any external libraries. By comparing the milliseconds since epoch using date.getTime() with the range of time between last Monday and next Monday, you can easily check for this:

const WEEK_LENGTH = 604800000;

function onCurrentWeek(date) {

    var lastMonday = new Date(); 
    lastMonday.setDate(lastMonday.getDate() - (lastMonday.getDay()-1)); 
    lastMonday.setHours(0,0,0,0); 

    const res = lastMonday.getTime() <= date.getTime() && date.getTime() < (lastMonday.getTime() + WEEK_LENGTH);
    return res;  
}

(calculating one week in milliseconds: 24 * 60 * 60 * 1000 * 7 = 604,800,000)

Discover a method to achieve this task without relying on any JavaScript libraries by following this resource: https://gist.github.com/user123/456789

Avoid link decay with the code snippet below:

function calculateWeekNumber( currentDate ) { 

  // Make a copy of the current date object  
  var targetDate  = new Date(currentDate.valueOf());  

  // Adjust the day number for ISO week date starting on Monday  
  var dayNumber   = (currentDate.getDay() + 6) % 7;  

  // Set the target date to Thursday of the current week  
  targetDate.setDate(targetDate.getDate() - dayNumber + 3);  

  // Determine the week that contains January 4th according to ISO standards  
  var januaryFourth    = new Date(targetDate.getFullYear(), 0, 4);  

  // Calculate the difference in days between the target date and January 4th  
  var dayDifference = (targetDate - januaryFourth) / 86400000;    

  // Calculate the week number based on Week 1 (January 4th) plus the elapsed weeks  
  var weekNumber = 1 + Math.ceil(dayDifference / 7);    

  return weekNumber;    

}

By implementing a clever solution without the need for external libraries, I successfully achieved this task. In this implementation, Monday is considered as the first day of the week. The function requires a date string as input and performs validation before determining if the provided date falls within the current week.

function isInThisWeek(livr) {
  const WEEK = new Date();
  
  // Convert delivery date to a Date instance
  const DATEREF = new Date(livr);
  
  // Check if the date instance is in a valid format (based on the function argument)
  if (DATEREF instanceof Date && isNaN(DATEREF)) {
    console.log("invalid date format");
    return false;
  }
  
  // Extract individual date components
  const [dayR, monthR, yearR] = [DATEREF.getDate(), DATEREF.getMonth(), DATEREF.getFullYear()];
  
  // Get the date of Monday
  const monday = WEEK.getDate() - WEEK.getDay() + 1;
  
  // Get the date of Saturday
  const sunday = monday + 6;
  
  // Start verification
  if (yearR !== WEEK.getFullYear()) {
    console.log("WRONG YEAR");
    return false;
  }
  
  if (monthR !== WEEK.getMonth()) {
    console.log("WRONG MONTH");
    return false;
  }
  
  if (dayR >= monday && dayR <= sunday) {
    return true;
  } else {
    console.log("WRONG DAY");
    return false;
  }
}

}

According to your comments, it seems that your week starts on Monday.

In this scenario, it might be helpful to determine the ISO week number for both dates and compare them to see if they fall within the same week.

To calculate the ISO week number, you can refer to this resource:

If someone's week begins on Sunday instead, you can utilize this guide to calculate the week number accordingly.

Subsequently, you could implement a function like the following:

function isSameWeek(date1, date2) {
   return date1.getWeekNumber() === date2.getWeekNumber();
}

function isDateWithinCurrentWeek(date) {
  const today = new Date();

  const firstDayOfWeek = new Date(
    today.setDate(today.getDate() - today.getDay())
  );

  const lastDayOfWeek = new Date(
    today.setDate(today.getDate() - today.getDay() + 6)
  );

  if (date >= firstDayOfWeek && date <= lastDayOfWeek) {
    return true;
  } else {
    return false;
  }
}